Link a creature's ability to speak to its Charisma rather than its Intelligence. All the other communication skills tend to be associated with CHA rather than INT - intimidation, performance, persuasion, et cetera... And as far as i recall in both of the MM books creatures that can not speak have and INT of 4 or below.
Use Charisma to determine the number of languages known. Bump dogs, corvids, parrots, primates up to an INT of 7-8. And you could do interesting things with telepathic creatures. Like ghosts having a high CHA and low INT, being incredibly persuasive despite speaking gibberish. Or mind flayers being really unpersuasive because they are low CHA and while high INT.
This isn’t actually a rule, and there’s nothing stopping anyone from doing what you described with ghosts or mindflayers, but I disagree about the rest. First, real creatures give us a benchmark for what ability scores mean. Chimps are generally estimated to have toddler-level intelligence, which puts their “IQ” so to speak at 20-25. The average adult has an IQ of 100, and one standard deviation is about 15 points. This gives a solid sliding scale for expressing character intelligence.
10 (+0) = 100, average
9 (-1) = 80, slightly lower than expected
8 (-1) = 60, mild mental disability
7 (-) = 40, moderate mental disability
6 (-2) = 20, severe mental disability, chimp/toddler-like
Bumping up creatures like chimps and dolphins to 7-8 makes the gaps between scores that much higher, and doesn’t allow us to express the normal human range of intelligence very well. While I think some creatures should have different ability scores based on their real-life counterparts, I don’t think the standard should be changes this way.
Likewise, I disagree with CHA granting more languages known, both because it’s less true-to-life and because INT is already the weakest ability score, and we don’t need to be taking things away from it.