I think your point (4) has substantial problems. I mean, as other commenters have already noted, hardly anyone in STEM studies formal logic. But OK. Let's suppose you mean "informal formal logic" -- not actual formal logic, but that sort of essential sense of how predicate logic works, that it becomes a backbone of much of your thinking. Math teaches that, as do subjects which are essentially math; but does the rest of "STEM" teach that? I'm not sure that's even true. Many quantitative disciplines look terribly sloppy from my point of view.

But let's get to something more interesting. Your point (4) appears to implicitly making the claim that learning formal logic (or rather, "informal formal logic") doesn't help much with informal logic. I don't think that's right at all. Learning that sort of formal logic is a great way to learn informal logic, and I think this works much better than the other way around. Doing any sort of serious math, you will learn how an argument really works, how to take it apart. Largely you will learn this from the numerous errors you and other people will make. ("Oops! I swapped the quantifiers!") You will see contradictions presented to you and have to find the mistake. I think it's easier to learn to spot errors in this setting, where you can say certainly what's right and what's not, and then move to the fuzzier setting.

Like, the arguments I see most people making most of the time are so bad, and they'd be better if they had experience with actually finding holes in arguments, and learned to apply this to their own. Well, that's what a mathematician does. In an informal setting, of course, almost everything is potentially a hole -- and so of course you learn to explicitly lay out your assumptions, ask the reader to bear with you or spot you an inference, and otherwise explicitly acknowledge where you're making a jump.

Because really, the worst errors in informal reasoning also pop up in formal reasoning. The biggest problem I typically see with people's arguments is equivocation. That's something you learn to spot doing math! And because terms in math are overloaded, you learn to break things down, to say, "OK, we've got 'continuous' in this sense, and 'continuous' in that sense...". Learning to spot equivocations and break down concepts would help people a lot.

My experience is that mathematicians, being familiar with this sort of thing, are in fact better at informal logic than most people, by a substantial amount.

I mean, I know there's the idea of the engineer who attempts to perform (informal) formal logic on e.g. politics, taking various statements as axioms and writing down the conclusions, without noticing that the terms used in the axioms aren't used in a consistent manner, or that the axioms are ill-specified, or that the terms don't connect to anything we actually care about, etc., and coming to ridiculous conclusions. And it's possible some forms of STEM teach that, this taking of imprecise things and treating them as if they were precise, because such people certainly exist (they're easy enough to find on the internet). But my experience is that a mathematician instead learns to notice equivocations, notices imprecision, and to actually do the work of taking things that are ill-specified and making them well-specified (when possible).

Basically, pretty much all the advantages people talk about for learning philosophy, to me seem to come up in math as well. The one big exception, I think, is learning not to take texts at face value, to wonder what the author is trying to accomplish by writing this. A math paper may contain errors, but you can typically assume it's a good-faith effort at truthseeking. Whereas that is something that's definitely necssary in other fields.