Lots of interesting posts, even though I disagree with 99% of every opinion presented here 
Hehe. I can't help discussing your opinion, which is obviously wrong!

So here is an unpopular opinion of my own:
I strongly believe that the piano music of J.S Bach should be played without ornaments.
I view
shoulds with suspicion, whether they tell me to do something or not do it. In my view, a
should relates to an objective, whether we realise it or not. So you should/shouldn't play the ornaments depending on what your goals are for your Bach playing - if it's to pass an exam it'll be different from enjoying the odd tinkle on the ivories in private or developing a modern interpretation. Should/shouldn't one play Bach in a jazz style? I see no reason to deny ourselves freedom of expression in music, as we do in other art forms. The unstated objective or injunction is often something like, "to be true to how Bach wanted it to be played," but (a) we've a dim view of that and probably always will have, (b) maybe Bach wanted us to run with his inventions and make them our own, or (c) maybe Bach wanted everything nailed down and as he intended it, but - were he alive today - reverse that opinion and realise he was too up himself.
If we go with "how the master wanted it" - and I'm definitely no expert at all - I've read that JSB came from an older tradition that valued freedom of expression and the player's interpretive judgement, whereas the next generation began to want everything precise and wrote books about how everything should be played (CPE Bach, IIRC, was a stickler for
the correct everything, from ornaments to fingering).
Of course there should be exceptions where the ornaments are “hard coded” into the music, but in every instance where there is a marking in the score of a “trill, mordent etc”, it should be ignored by the pianist.
That leaves logical room for contradiction - unless you mean by "hard coded" the ones written in original scores, where we have them. "Should" we always use the autograph or check if the modern edition we've got matches it precisely?
Why?
Not only will the music be much easier to play, but it will also be MUCH more beautiful and mature.
Sometimes doing something hard is better, and beauty is in the ear of the beholder. It also depends on the instrument chosen, particularly what kind of sustain it has. I suspect that the preponderance of ornaments in Baroque music might be down to the popularity of the harpsichord, clavichord, lute and - as much of Bach's music was probably written on and for - the lute-harpsichord, with their relatively short sustain and little dynamic range, leaving rather boring holes in slow pieces unless an ornament is added to extend the note. Some Eastern string music - balalaika? - might play the same note repeatedly until it's time to change to the next one in the melody, but that's awkward on a keyboard. So, on a bowed instrument, a Sarabande can be gorgeous with minimal ornamentation - a long note can sweep in, sustain for seconds, even get louder to a final short stop - on a harpsichord it just goes plink. And you
do want to cut through the murmuring of the restless bewigged throng in the drawing-room, after all.
Besides, the alternating notes of ornaments add to the harmonies that are playing and make a richer sense of it.
The insistence of realizing all the ornaments in Bach’s music is simply extremely childish and stupid. It shows not only a poor taste when it comes to performance , but also, more worrisome, a serious mental immaturity that that has infected even the most renown music establishments responsible for teaching the younger generation of pianist.
(I hope I don’t need to go into hiding after publicly stating this opinion)
I agree with your view that having to play them all is stupid, I just think reversing that is no improvement.