I’d argue that even if Twitter wasn’t obligated to embrace the principle of free expression, they’d have a strong financial incentive to adhere to the principle of free expression. Sure Twitter could theoretically limit discussion to whatever topics they wished. And they could even limit users to tweeting about different types of wood. But if they did, you’d only attract the wood aficionados while everyone else left Twitter for greener pastures.
It’s an extreme example, but the point I’m making is that if Twitter limits the acceptable range of expression and viewpoints, then people will start to leave Twitter of their own volition. And Twitter lives or dies on it’s total daily user count. If that number decreases, then they have to sell ads for less, because companies have fewer eyeballs looking at the products for their ads.
So if Twitter bans people merely for expressing viewpoints that the support overlords don’t like, a large chunk of the population will feel like they aren’t wanted, and they’ll leave. Twitter will be cutting off their nose to spite their face. And it would be utter foolishness.
Unfortunately, Twitter seems to be run by fools, so this will probably happen at some point.