I think that part of it may be how music is recorded and produced these days.  There is a tendency to give it a certain sound.  

But often, when FM or other people put up videos of how to play something, it has more personality and "life" to it.  I was watching a video on youtube of Itzhak Parlman doing the Devil's Trill, and I felt it had a lot of life and personality to it.  But still very different in some ways from recordings of Shumsky doing the same piece. 

Other than style being a little different, the Shumsky recordings felt a bit darker and warmer, which would be probably the acoustics of the place he was playing in and the recording techniques and equipment of the time.  Modern techniques and gear are "cleaner" and usually a bit "brighter".  Part of that is recording styles having changed, but part is that the older material was recorded on tape or cut directly to the master disk rather than digital.  Also, the older recordings were made with equipment that used vacuum tubes/valves instead of transistors, and there is a sound difference there too.

Maybe also players have changed, and perhaps focus a little more on technical accuracy than on expression.

Well, the girls in gossamer pajamas jumping about are fun to watch.  I'll bet Mozart would have been delighted and composed pieces just for that, if he could have seen this far into the future for a few minutes.

I do have to agree, though, that I take such stage shows less seriously as regards the music.  They can be good musical entertainment, but with all the jumping about, I do not expect them to show the same degree of prowess as Perlman, for example.  On the other hand, I would NOT like to every see Perlman in gossamer pajamas. LOL

I personally do not have any aspirations towards making a living as a legitimate violinist at my age.  While there have been older violinists who are of note, they did not *start* on the instrument at 51. 

Besides, I am not very acrobatic and would look dreadful in gossamer pajamas, so that direction for a musical career is just not an option. 

Having thought on the matter a bit, I think part of the difference comes from the focus there seems to be these days on making "child stars" and expecting musicians who are sometimes very young to perform as if they have decades of life experience.  There is too much of a focus on not messing up, rather than people playing who are just in love with the song and the sound of their instrument.

On the life experience point, could Mr Bocelli in the clip you posted do the song with the same feeling if he had never wooed a lady with a song before?  He could hit all the notes and do the same expression with voice, perhaps, but could he mean it?  Or would he be imitating someone from long ago who meant it?

Some very young "prodigy" may be able to play all the notes, but they haven't had the emotions or experiences the composer was writing from and nothing comparable in their lives yet.  It is cute for a little kid to sing a love song, for example, and may show they have considerable talent, but it won't be their emotion that is in it so much as an imitation of the emotion of some adult whose notes and expression are being copied. 

At the risk of being thought of as silly or overly poetical, playing music is sort of like kissing.  You will usually do better at it and enjoy it more if you sort of fall into the experience and let the world go away for a few moments rather than thinking about it too much and trying to not do any of it wrong.