This question is important enough that there have been papers written on it. I suggest you read https://pubs.aip.org/aapt/ajp/article-abstract/65/6/501/5300... which may strengthen your understanding.
This is a physics education journal: its papers are supposed to be interesting and accessible to undergrads, not on the frontier of the field.
What the linked paper amounts to is noticing that the sensitivity of a detector depends on the relative length scales of the arms and the waves you're trying to detect. This is true, and also one of the first things you would consider when figuring out what size your detector should be. It's a good homework problem, but not news to anyone actually working on LIGO.
> No clue why GP thinks it "shouldn't work"
It's also possible you think that this is all about laser interferometry, and aren't properly considering how it could work in the context of compressing space, since a laser interferometry system in compressed space wouldn't produce interference.