The reason burden of proof is on the person making the argument is that it is trivial to come up with arguments that are not falsifiable. And for any non-falsifiable claim you can make a contradictory non-falsifiable claim.

So if you can accurately say of some claim "there is no evidence of that" then the claim is completely refuted. Thus asking for evidence is a polite way of pointing out when something is completely made up.

Sure, if someone makes a claim that is widely established, like climate change or natural selection, then of course some rando on the web asking for yet more evidence is probably trying to derail the conversation.

But if a claim is not widely established, like intelligent design, then a request for evidence is perfectly reasonable. There can be no a-priori convincing counter argument without referring to facts in the real world. Indeed, almost not claim is refutable a-priori without real world facts.

So given an unreasonable and unsupported claim on the internet I suppose we can 1) assume the poster is a troll and ignore them or 2) assume they and the audience are genuine and point out their statement is unsupported and therefore false. Whether one actually wants to go around correcting people being wrong in the Internet is another question. But a guy's gotta procrastinate somehow.