Private schools are NOT forced to accept vouchers. Your cry of “egalitarianism” rings rather hollow.
Ending the wretched government monoply on the bloated public education system is very good thing. Right now tax dollars are flushed down the toilet when they are spent on pubic schools. You wish to keep that system in place. That is not defensible.
It might be a good idea to enlarge your social circle. The ideas you have stated are often rightly associated with anti-social cranks, and I don’t suspect that you are such a person.
You're claiming "monopoly" while at the same time arguing that vouchers should pay for the alternative which exists, which is private schools.
Maybe a dictionary lookup of the word "monopoly" would help this argument.
You wish to keep that system in place.
No, I'd like to see, for instance, the Chicago Public Schools abolished and the earth salted. Other than my property tax bill shrinking, we'd hardly notice the difference