How does that prevent anything? You'll still have the exact same issue. Unless you think a google employee would be the same class as a small mom and pop employee just because they both own a share of their workplace.
If you look at it through a lens of a specific theory that may be true. But that theory does not apply nor translate to reality. Everyone already owns captial its called a 401k or investment fund. There is still class. If that was taken 1 step further and everyone owned a part of their workplace there would still be class. Being forced to own your workplace reduces mobility and traps people. Shutting down a coal plant would just cause 1000 layoffs it would financially destroy 1000 people. Its a stupid idea that only children still believe in.
If everybody owns the means of production and everyone participates in the labor force, class distinctions disappear.