I think this misses the confounding variable.
What maintains grammatical complexity seems to be centralization. There's an age-old debate about whether grammar is prescriptive or descriptive. I'm in the latter camp, which is to say that if enough people say something "wrong" then it's not wrong anymore.
Education however tends to be prescriptive. It teaches and maintains an existing way of using a language, so much so that in some places the colloquial and "official" versions of a language are esentially two different languages. The "many linguists" here ascribe this to a "society of strangers". I think the reality is that absence of a central authority means languages tend to change faster and thus lose unnecessary complexity.
English is a great example of this. English is a Germanic language. Old English and Old German are very similar languages. After the Norman invasion in 1066, hte official language of the English court became French and remained so for ~300 years. This was the period of MIddle English.
After this came early Modern English (eg Shakespeare). While Old English is essentially unintelligble to the modern English speaker, a lot of Middle English can be understood.
But that 300 year period made English grammar much simpler. Most cases disappeared. Word order became fixed. Noun gender mostly disappeared (other than pronouns for people). The subjunctive mood mostly disappeared (eg "If I were king" instead of "if I was king" is about the extent of modern English subjuntive mood). The last vestige of genitive is mostly just adding "'s" to things (with a few exceptions of course).
English spelling and phoentics is of course a complete mess. So are tenses. But absent central authority we stopped having to know that a table was "he" and a chair was "she" (made up examples; I don't know their gender in Old English). Isn't that interesting?