I can't say I agree about Barbie (I liked the film, but think better films are in competition). However, I take your point about the inevitable subjective judgements at play. I wish the criteria were free of politics (and envy) too. I don't believe in "paying dues" so to speak. If you make a great film and it's your first, that should be rewarded (Citizen Kane, for instance, which wasn't).

In Gerwig's case, I was a lot more annoyed when she wasn't nominated for Best Director for Little Women. I'd have happily ousted Quentin Tarantino or Todd Phillips from the line-up to make room for her that year. But for Barbie? Nope. The other nominated directors are stronger (in my not remotely humble opinion). :)

More of my thoughts on the matter can be found here, if you're interested: https://fanfare.pub/should-best-director-nominations-automatically-follow-best-picture-nominations-50c92c87a97b