You saved me from posting this. Strict word order makes a lot of things easier that have to be done through morphology in the vulgar Latins.

> Languages with richer morphology may also have smaller vocabularies. To be fair, this is a contested conjecture too.

I agree with the criticism of this to an extent. A lot of has seemed to me like it relies on thinking of English as a sort of normal, baseline language when it is actually very odd. It has so many vowels, and it also isn't open so has all of these little weird distinguishing consonant clusters at the end of syllables. And when you compare it to a language conjugated with a bunch of suffixes, those suffixes gradually both make the words very long, and add a bunch of sounds that can't be duplicated very often at the end of roots without causing confusion.

All of that together means that there's a lot more bandwidth for more words. English, even though it has a lot more words than other languages, doesn't have more precise words. Most of them are vague duplications, including duplicating most of Norman French just to have special, fancy versions of words that already existed. The strong emphasis on position in the grammar and the vast number of vowels also allows it to easily borrow words from other languages without a compelling reason.

I think all of that is enough to explain why English is such an outlier on vocabulary size, and I think you see similar in other languages that share a subset of these features.