Thelonious Monk’s Tips for Musicians (1960)

Right. The conductor will hate seeing you tap your feet. So just don't let them see.

You are correct that keeping time (what an engineer would call "maintaining a common time base between transmitter and receiver") is necessary to play together with other musicians. But what musicians would call "feel" is what an engineer would call "phase modulation" -- whether a note is ahead of the beat, on the beat, or behind the beat; and by how much. Especially in Black American music (jazz, blues, soul, R&B, and a bunch of pop that's been influenced by those styles), there is a lot of crucial information there beyond what is conveyed in the "gridded" rhythms that are conveyed in Western musical notation. If you are not aware of this, you will still have problems playing with other musicians. From personal experience, it is anxiety-inducing to play with musicians who are ignorant of their beat placement and as a consequence have what an engineer would call "jitter" -- their timekeeping is correct on average, but on each given beat, they might be a little bit ahead or a little bit behind. You can play with a metronome for ages and never realize you're doing this wrong, as you're not consistently rushing or dragging, you're just inconsistent.

I agree wholeheartedly, but I actually lump this in my head under "rhythm" rather than "feel". One of the reasons that black musicians tend to have on-average better is that they often have spent a lot of time physically dancing or playing live gigs at church/with their adult friends, and had to learn how to place notes just by hearing other people do it. This is a more effective method for training feel/rhythm than showing someone note durations on a sheet of music and telling them to figure it out themselves.

I think the way to correct the bad "feel" habits you're talking about is to play a lot with talented, on-beat musicians who will correct your playing in rehearsal. They will also assign you parts that you can handle that serve the sound of the band, rather than serving the intentions of the composer per the sheet music. Another issue that young western musicians have is that they most often play with other players at about their skill level, which stops them from being able to quickly learn good habits from better musicians.

good video from adam neely explaining this list

Imposed on top of this is a culture of treating it like a contest. This is an easy trap to fall into, because the repertoire is organized by difficulty. But I quickly noticed that the most laid back parents were the ones who were performing musicians themselves. I'm a performing jazz musician so my kids have heard me play plenty of clams on the bandstand without stopping. ;-)

The parents have to get out of the habit of stopping their kids when they make a mistake. I read a comment from a famous teacher, that he doesn't stop his students when they make mistakes, because it kills their flow. Unless the mistake is repetitive. Isolated mistakes are not teachable, repetitive ones are.

My daughter's teacher had a really nice thing, an open recital at his house every Friday evening. Because it was so frequent, kids could just show up and play whatever they were working on.

There are alternatives to traditional classical teaching. In addition to their classical lessons, my family has gotten into fiddling. That's a totally different vibe. We went to a fiddle jam, and recognized one of the fiddlers from the previous night's symphony concert.

Now for my own opinionated opinions, not necessarily contrary to yours: 1) At least in classical and jazz, a player has to get over the hump and learn to play in tune at some point. In any event, intonation problems typically reveal technique problems. 2) "Feel" is not orthogonal to technique. Wherever the note belongs, your brain and body working together have to put it there. And "feel" is anything but absent from classical music -- you just have to listen harder for it because it's more subtle. You can hear it when it's too rigid.