You absolutely can, and that's even been a norm in the US since CDA Section 230 was implemented specifically to make that possible, within certain bounds, which Twitter sits well within.
Admittedly, that's been progressively chipped away recently.
Joe Biden is for the idea: https://www.nytimes.com/interactive/2020/01/17/opinion/joe-b...
The government being selective about which expressive choices by a platform operator are get favorable treatment under law rapidly gets into violations of actual Constitutional free speech protections, unlike the private actions that people are making fake “free speech” claims about.
No, it's not. Permitting private bias without government consequence is the definition of free speech. Restricting it is contrary to free speech, and is permitted only to the extent that it fits within recognized Constitutional limitations on the right of free speech.