Aren't the videos enough practical evidence? I mean, if transposing with the old notation was super easy why aren't there tons of videos like it on youtube? That's practical evidence for me.
If you want theoretical evidence, let me indulge you: Let's say you'd have to go on stage in five minutes and have to transpose a piece (doesn't matter what genre, Scarlatti sonatina, Duke Ellington standard, Bach fugue) to a key randomly determined by the audience. Playing on a real piano with actual strings, and not a digital one. You can either have the piece in C-major or A-flat-major. Of course, most musicians would rather pick the sheet music in C-major, because it's much easier to transpose from there. That's a clear evidence that Puck's notation has an edge over the old one, because it's practically always in C.
Same goes for musical analysis.
Same goes for reading music. I mean... Major and minor chords literally look the same in the old notation. You always have to refer to the accidentals in order to determine what is what. Why cast two glances instead of one?
About what that other Mister said about fingering: It's not like the old notation magically makes any pianist play the correct fingering at once. (There are different hand sizes after all. I have fairly small hands for a woman, so my fingering is going to be different than, say, for a male concert pianist.) That's why people used numbers in order to indicate fingering.
More evidence: Play a random melody to any musician. If they don't have perfect pitch (and the vast majority of professional musicians does not, I don't, I presume you don't either) they'll write down in eleven out of twelve cases (because there are twelve keys) something that's objectively wrong. – If you say now: "Well, then let's write out everything in C-major, so that doesn't happen"... I applaud you, because that seems like a first step towards Puck's notation then.
Also, you'd need ruled paper. Makes it less likely people compose. Written evidence.
I can probably think of more. How about you show us how well you can transpose music in the meantime (I propose Mozart's second piano sonata, second movement, link is here:
https://imslp.org/wiki/Piano_Sonata_No.2_in_F_major%2C_K.280%2F189e_(Mozart%2C_Wolfgang_Amadeus))?Or if you'd rather avoid it... well. Then this forum seems to be for 'theoretical musicians' only. Didn't know those were a thing.