I say legally. A broker-dealer should be required to either give advanced notice of a suspension like this, or have a clearly upfront volatility metric that triggers it. (No, a TOS statement like, "We reserve the right to suspend trading at our discretion" is not a clear rule. It's a weasel clause)

Users would then know, in advance, if a particular ticker will be restricted. Either through specific advanced notice, or because they were told that all securities that exceed a volatility of X over Y time period will be restricted.

Whatever the rule, it can't be a snap decision that leaves users with no recourse.

If you're not an appropriate day-trading app, then don't act like one until you suddenly don't want to be one anymore. Make the rules in advance, communicate them, and let the market decide if you're appropriate for their needs.

Again, is this based on any real legal foundations, or on what you think the law should be?

What I think the law should be. I'm not qualified to say if there is a legal violation here (whether criminal, regulatory, or civil).

I said in another comment that my thoughts on this are in the "ought" category, not the "is" one.