You get to choose your school.
Now if you want give a voucher for 1-2k for schools that cost 5-10k don't try and pass that off as school choice.
In other words you mean "full" school choice as apposed to partially covered school choice. But this is definitely real. It's just only partial.
Also, I have no idea what the local governments allocate for public school per child, but it would not be reasonable to expect more than that even if your school's tuition is higher.