RE: Violin improvisation
Oooof, I'll try and answer as best as I can in the time I have!
From the performer's side of things. The lack of judgement does encourage people to inprovise and ornament more, this is important because in a profession where the majority of work is freelance, the incentive is to "don't rock the boat" instead of taking risks. Even if they are not ornamenting, there are more risks taken with timbres of sound and interpretations, which makes for a better more entertaining performance as a whole.
Unfortunately, it is difficult for an audience to really notice this sort of thing. We never perform side by side with another ensemble (just not normal in Classical music), so it is hard for audiences to compare and see what they like. Also, audiences (and musicians) have been brainwashed in a way, via recordings and the prioritisation of perfection over communication, to expect and desire performances that are in general non-offensive. Of course, I'm speaking in a general sense, so it is not true across the board, but it is the trend.
Results improve of course, with practice comes the refining of skill. Learning what works and doesn't work. However, the practice is made more difficult as we cover repertoire from over 2 centuries from a multitude of countries. Each country and time era has it's preferred style of composition and improvisation/ornamentation. In the interests of not making t he music sound "weird" but adding embellishments that are "out of place", we do need to study and learn about what is appropriate or not. This learning informs our feeling of what is "natural" or "in good taste".
That said, some players have better affinity for certain styles and times . Speaking personally (@bengy), I think I have a better affinity for the High Baroque and Classical styles. Earlier music I love, but I know I am weaker (in a relative sense, compared to myself in later eras) , and I appreciate that other people do divisions and such things much better than I do!
Thank you for your extensive answer response! Gives me a better insight in your thoughts and experiences around improvisation. Some of my friends are electronic producers and DJs and I discovered similar things in their segment; Most people dont know what these guys are doing behind the decks or computers, so for most the music just needs to sound good (generally: not too complex, and a good beat), regardless if the DJ is doing a lot of work, or almost no work. The music fans (certainly not all at a dance party, most of them not actually) will like to know more, and when you tell them the artists will play live (as in creating all the tracks on the spot using samples, effects and all; when done in the correct way, this is to most improvisation an artists on stage can get in the dance music world), or will do something other than usual, these people will be on top of it, to hear if something unique is created, and to determine if they like it or not. But the mass, well, they just want to hear a beat (ok, this is a little but black and white statement, but still, not far from the truth).
No problem, it is a pity that the audience (again in generalities) want something that is safe and inoffensive. It is not good for the performers, as it really discourages risk taking and encourages a mediocre, almost detached performance.
The way we try to help the audience understand what we are trying to create is by talking between the pieces, to try and focus what the audience patterns to.