Converted to jazz, rock...?

There are many talented jazz and rock musicians who thought themselves how to play a particular instrument...
I believe that it's possible to teach yourself to play guitar. Trumpet and Sax is OK too, but you'd better have some previous background with different instrument. My friend played a violin... Let's say he was a drop-out student getting bored from Bach, Beethoven, Mozart... He decided to play jazz, rock and folk music with violin and than tought himself to play sax and than later-on to play trumpet.
To teach yourself to play piano I believe is barely possible with preference to have a previous background and ability to read sheet music(which i hated the most times back...). I believe that most of the jazz and rock piano players have their musical education which I assume can be also incomplete in some of its degree(of incompletion).

Now to the questions:

Why people think that the individual with classical music background sometimes is very unsuccessfull in jazz or rock? I cannot imagine myself a piano player who did not excersise with ethudes of Schuman. I believe they give a basics to the improvisation. I cannot imagine any musician on any instrument without "warming up" berfore he/she starts play something and ethudes is probably the best way to deal with it.

I'm also curious about musical education whether you can start from Beatles or Mulligan instead of starting from Schuman or Rubinstain?

I also know that there is such credit you can take as
"basics of improvisation" but I believe that improvisation is something that comes from inside and should have rather a personal approach. Whoever took or takes the personal approach has its own signature on which people distinguish him/her from different musicians.

And finally what is the best way to become a rock or jazz musician?

Plan a)

Start musical education with basics as any musician starts in the school playing some ethudes and sonatas and than drop-out without wasting time and start rock or jazz when you feel yourself strong.

Plan b)

Get yourself onto the guitar and bass way by teaching yourself with different or one private instructor... There is a possibility for you to get kind-of monophonic improvisation with no personal signature unless you're born guitarist or so...

Plan c) Get yourself a complete musical education, play in some orchestras or conduct it; getting bored of this start improvise and get to the stage with rock or jazz band. Probably too long but if that's that case there are more possibilities to improvise using stronger and more sophisticated techniques(probably grabbed from Schuman ethudes with 64th notes or Rachmaninoff for instance). If people believe that in this case the musician is only adopted to read from the sheet, well, it's again either yes or no imo.

And finally, the question:
Can you feel that your son or daughter is a born rock- or jazz- musician from its childhood?:^)

P.S. for vocals is the whole different story where I tend to agree that singer with opera background less-likely to be successfull in jazz.