Why did guitarists invent TAB?
Because the genres which dominate music today [amongst the general population] are usually composed by being recorded not scored - and the motivation for becoming a musician in those generes is, again in general based on simple techniques, simple harmony, improvisation, and creativity. Rather than, in comparison - playing some established "rep" that has a huge technical requirement which requires years, if not decades to get to a stage where you have the technique and musical knowledge to interpret music that was composed by being scored.
Yes? To be a rock god, I have no need to read music, because I generally need to play my own pieces to succeed and not someone else's. But the stuff I need to learn to do that isn't particularly taxing theory or technique wise. Single-notes played, sometimes extremely quickly over chord progressions that generally have no thirds [so you can't hit a wrong note, major or minor] is probably the most advanced technique required for rock - and the big point of that is that you are supposed to improvise when doing it, not read a score.
Nevertheless, in spite of the fact that to be a guitarist in, say, rock, you need to play your own pieces, some guitarists, as you tube will testify, want to play those pieces they like from their "heroes"
Hence the problem. The pieces aren't scored - there is no music published. Quite often the guitarists won't even play the same solos and fills each time they play.
But creating sheet music is difficult. Try it. If you want to type in some music here you'll get stuck and start writing C D E and so on, perhaps with numbers to indicate octaves. This is a problem you haven't solved. You still need silly plugins and windows whatever software. Note how, by comparison, I can blather away in a multitude of languages using "text" and it works with just about everything. No magic software required to give you guitar tab. If you'd done that with sheet music, you might have a point or purpose.
So, the way to learn guitar music is to listen to the recording or other players. Which you'll note for 99.999% of the easy end of classical music doesn't exist. The ABRSM does some recordings with its books, but whilst you can probably buy the entire piano rep grade 8 and way beyond 10 times over for less than a fiver these days [if you aren't to fussy about the pianist] you'll be lucky to find any recording of a few simple pieces [at least pre-youtube]
Now as you are probably realising yourself "why tab" it's because getting the tab for Steve Vais song "look at me I'm bloody fantastic at playing, I am, and I've still got all my own hair" tab is, unlike the not-a-problem-in-the-first-place you're trying to solve, a very difficult thing for ordinary mortals to do. You need to transcribe it first - and this is why 99.999% of guitar tab isn't just wrong, it's obscene

They lose everything - all the stuff that guitar tab doesn't have, and then they get the bit that's left wrong in a way that's more than just wrong notes.
If any argument wasn't going to work it's suggesting guitar TAB. Guitar tab sucks.
[Actually that's not strictly true, you can these days buy books of transcriptions, because the extraordinary individuals that can transcribe want to eat, like the rest of us, but since these books have both tab and sheet music in anyway they negate the point you were trying to make with your question and thus aren't relevant - unless you ask "why sheet music as well?"

]
So, guitar tab sometimes shows the correct frets to hold, in a way that could easily be recreated on a text based medium [like the internet. Yes it has pictures and videos and so on now, but maths and sheet music are still barely capable of being expressed via it. Especially compared with things that were invented for it, like programming source and guitar tab]
It shows it to someone who cannot [yet - generally books on guitar talk about developing the skill] get the notes from the record and who doesn't necessarily know the notes on his instrument either. Thus s/he cannot transcribe a middle C note to which string / fret [which, as you know will often have more than one possible choice too] he should play. Guitar TAB shows exactly where to play on the neck [although as often as not the transcriber picks the wrong choice - I've no doubt there are guitarists struggling to play pieces that, as transcribed, are difficult if not impossible to play yet, in reality and played correctly, are fairly straightforward, and make much more musical sense too]
But, TAB only works so long as he/she knows the piece [i.e it works if they can get 99% of playing the piece from listening to the recording of it, because the tab doesn't express it]
In short, it wasn't invented under some clearly false and asinine premise that by using it, it would make learning to play the guitar easy [or easier] Nor is it, in any sense, a replacement or alternative for sheet music [outside of the very limited role it has described here]
...and of course, classical guitarists, along with many good rock / jazz musicians, guitarists and so on, learn to read music.
Lastly you'll note that you tube, recitals, auditions, rock concerts, classical concerts and many other similar things show us that the vast majority of musicians, good or bad often sit and play without any sheet music, tab or whatever in front of them at all. Why invent "no sheet music at all? " Proving my new invention "blank pieces of paper" would work
No, what it does say though - it speaks loudly about the difference in time taken between reading the score, and being able to play it well. The time taken to do the latter is a large part of why, even those of us who aren't especially talented, manage to memorise the music we play without any special effort - because we have to play it over and over and over.
In short, it makes absolutely no difference how long it takes to read the score - and, profoundly, this is more true with the less skill you have in playing the piano - plus, the more you read it, the better you get at reading it - in essence you'll read music long before you'll be able to play it. I've no special talent, in fact, I'm the most useless and poor musician I've ever heard, nevertheless I can still sight read music several grades higher than I can begin to play.
That's without any special learning, education or classes. Simply being shown FACE and so on, and then starting with simple pieces. Yes, sometimes I've had to go "err, c d e..that's F" and thus I read the score extremely slowly - but note that same piece takes weeks and weeks of practise, I soon know every note...the next piece of a similar level, the score is easier to read.
Your notation is no different. No easier. I've used it.
The mountain I might have to climb to read more difficult music is tiny in comparison with the decades of practise I'll need to be able to play the pieces it describes.
Indeed, like many people do, as you note with the huge drop out rate, I'm soon likely to give in because no matter how much I practise I cannot play the piano. What I play, even without music, even for stuff that I don't need the score any more, sounds like sh*t. That's why people drop out. It's simple really - we practise, myself sometimes up to 8 hours a day and don't improve. Thus, still cannot play simple pieces well.
Worse of all, sadly, for whatever reason, teachers like yourself have nothing to offer which will help. Whether that's because you're all clueless as to why some of your students learn and some don't I don't know, but I can pretty much guarantee that it's sweet fanny adams to do with the sheet music and if that is your organisations motivation then you're wasting your time.
The failure rate will be exactly the same TN or not. If not worse. If you want to find the people that can play piano it's no different to why there are sports in some countries which have few good players. You need to get lots of kids playing piano and then you'll find the ones with the talent. Inventing asinine gimmicks and methods designed to turn the few kids that start but, like me, cannot play no matter how hard we try, into pianists is never going to work. Your notation isn't going to increase the number of successful musicians.
TBH, IME these gimmicks and things just tend to lose the authors credibility amongst their peers. Even if the person is otherwise a good musician and / or teacher. It's no different to "play piano in an hour!" "Play POWER piano' - we all know the author, if they can play, is just trying to make some money from no-hopers like me. They didn't learn to play using their method and neither will any good musicians.
That the huge drop out rate is linked to sheet music is a completely farcical notion. Anyone selling a notation claiming it makes playing the piano easier using that kind of logic is, imho, being completely dishonest.
They might get away with an [still arguable] claim about whether what they have makes reading music easier or not. But there's no question at all that playing the piano isn't made easier by changing from one kind of sheet music to another.