Hi Vyshakh, you see fine tuners on less expensive violins because it is assumed that a student will be playing it, and will need more help tuning the violin. Advanced players use the pegs only to tune, using the fine tuner on the E only. Advanced players are more likely to have a more expensive violin and can tune their violin with the pegs, so fine tuners are not installed.
When tuning a violin with the pegs, turning the peg just a tiny bit makes a big difference in the pitch. There is also the complication of having to push in while tuning to make pegs stay in place. Most students will have a lot of trouble with this. They often try it and break a string, or didn’t realize the fitted peg needs to be pushed while tuning. Fine tuners are just for convenience.
The E string is most apt to break while tuning with pegs because it is the thinnest and often only made of steel, not a stretchy material like Thomastik Dominant Violin Strings.
A professional can tune most student violins with pegs only. The fine tuners are there so a student can safely maintain the tuning between lessons. Using the pegs just needs to be taught and supervised until the student feels comfortable enough to abandon fine tuners on lower strings. But no hurry!