Because the solutions proffered aren't ways to be a non-renegade wizard unaffiliated with the Towers of High Sorcery, they're ways to justify a character surviving as a renegade wizard.
Fundamentally, I don't buy into the premise of there being only a single wizarding order that has an ironclad monopoly on practitioners of the arcane. Do the elves not have their own archmages? Has no king ever taken issue with the idea that their court wizard (assuming such exists) might be more loyal to the Towers of High Sorcery than to the crown they claim to serve? Has no one in the Towers ever argued that maybe the way they do things is somehow wrong? Have wizards declared renegade by the Towers never banded together for safety? Are there no independent wizarding schools on the other side of the world?
The idea that these are questions that Dragonlance just...doesn't think it necessary to answer, or seemingly even consider, simply baffles me.
There are novels that answer a lot of them, I don’t think you find them in a setting book however (maybe the one specifically about the towers, no idea though)
So let’s go through them a bit (to the best of my knowledge)
1) elves do, they are also members of the towers, those are not exclusively human
2) kings do take issue, but there is not much they can do about it - other than get lucky and get one that turns out more loyal to them than the towers (you get your wizard assigned by the order…)
3) no idea, if so, then not successfully

They had a good reason not to change, a renegade almost caused the end of the world, made them much more vigilant - I’d argue that changed again with the Cataclysm though (logistics…)
4) yes, but they are few, so it does not really help
5) no idea, none that have their wizards end up on Ansalon at least, apparently
As before, what is stopping you from going that route ? Check with your players if that deviates too much from DL for them to enjoy it and if not, run with what you want.