I think it needs to be defined with more specificity than "blatant doomerism", both to make it more clear when to enforce rather than "I know it when I see it" and also to prevent unfair bans to people talking about something that's a bummer in good faith.
I don't think an environment of toxic positivity is healthy and I fear such a broad definition could foster one, i.e. "oh I can't say that or I might get banned"
on the whole though I like the idea of an additional rule added of the sort. it doesn't seem like the person(s) in the first examples given was saying anything in good faith.
I also think the punishment should give a lot of grace, like first a warning and comment removal before any ban.
edit: a word