You keep assuming that "private" means they are not accountable to the general public, and that they are (fantastically) standing alone without leaning on the resources that all of us are providing.
And that's simply a complete mistruth (I'd call it delusional - in the case of tech companies). They might be private companies, but they cannot (literally - full stop, without room for debate) exist without the infrastructure that we are providing them.
From the roads that they use to provision their datacenters with equipment, to the power we generate with power plants under government supervision, to the police/lawyers/judges that ensure their property rights, to the firefighters who deal with their emergencies. To the cable companies that we subsidize to provide them internet, and connect them to their customers. To the trash we collect from them, the water we provide, the clean air their employees breath.
I don't understand how you keep missing this point. "Private" does not mean self-sufficient, and it is an insufficient standard to claim that being "private" means you have carte-blanch control of how you operate.
This is why we have regulations over all sorts of industries. Do you think private companies are free to ignore accessibility laws? Or that they can violate discrimination laws? Or that they enter into any contract, regardless of the clauses?
Basically - "Ownership" is only a concept that exists BECAUSE we enforce it. There is no such thing as "ownership" without the participation of all of us in this make believe game.
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So in this case - it's complicated. I think in general I don't mind private companies being allowed to remove users from their platforms, but I think it matters quite a bit what sort of impact that has on the user, and what sort of actions provoked that removal.
Should a store be allowed to remove a jewish person because they are jewish? Nope - damn well shouldn't.
Should a store be allowed to remove a jewish person who is breaking shit and making a mess? Sure.
Should discord be able to ban malicious users spamming other customers? Sure
Should discord be able to ban a user because they changed email addresses? Probably not.
Intent and actions of both parties MATTER.
And simply claiming that it's "Cost efficient" to not deal with problems that are trivial to a company, but utterly life changing to an individual (such as loss to a primary communication channel) is not acceptable. It's cost efficient for the company, and debilitating to the individual - they are harmed immensely so the company can save pennies.
We've long had established law around unequal bargaining power (it's where roughly all of our labor laws come from...) and it's been a concept for literal centuries.
So I'm inclined to say this on the matter:
Just because they currently "can" remove a user for this, doesn't mean that - ethically - we should allow that practice to continue.
It just means our laws are woefully out of date for this application, and technological progress is outpacing political progress.
Edit: Basically - I'm claiming complete and utter rubbish on this
> First off, this is a flawed argument because my taxes don't pay for the servers running Discord or other similar services.
Our taxes DAMN WELL DO pay for discord to be able to run their servers. We pay with our taxes, our time, sometimes our lives - so that the environment in which discord runs their servers can exist at all. Just because discord happen to be paying the costs for the servers themselves is almost immaterial. Society is an organism. We are all part of a whole.