Never really like this because it feels some arbitrary as to what counts as making a claim. Human language is filled with implications, and those implications are filled with implied claims. Yet burden or proof seems mostly used when someone makes one of those implied claims explicit, say by explicitly rejecting one.

"We should do X."

"X is not possible."

There was an implied claim that X is possible and an explicit claim that X is not possible, but often it feels that in such a scenario, it is the second individual who is deemed having a burden of proof.

This is made all the worse that there is rarely a single implied claim, but more a group of related implied claims that are also weighted. Like some combination of "data centers don't destroy the environment" and "or maybe they do, but only in amounts of destruction that are tolerable compared to human behaviors and worth the outputs gained" and even "they modify the environment, but it doesn't count as destruction, just change". And even worse (yet again), different readers of the conversation will find themselves placing different weights on these different interpretations making it near impossible to agree on what the original claim is. Thus the first person who makes an explicit claim gets all the attention which ignores all the messy implied human communications preceding it.