Interesting, I mostly agree. Criticising someone for their appearance or how they talk is kinda shitty but, just as thought exercise, what are you thoughts on Elmer Fudd? Should he be cancelled?

think their speech impediments are hilarious and that we're all secretly laughing at them, but we stifle that laughter out of politeness and decency

Not laughing at them, isn't it more the case the humans just find some sounds amusing and interesting when they are different from the norm? But it depends on context so if it isn't appropriate we don't signal that we are amused?

Aren't some accents or voices amusing? If someone walked up to you speaking like Joe Pasquale would you not find it a bit funny or amusing even? You might but you are likely to stifle the laughter because you're not a cunt or 'out of politeness and decency' as you said.

Now, what if the same guy approached you and was being deliberately offensive and nasty? Might you laugh at him? Maybe. Might even say 'fuck off, you sound like Joe Pasquale'. Now, what if they sound like Elmer Fudd? Probably a similar outcome.

The intent is clearly not to be offensive to all people with speech impediments? Maybe but I think people with speech impediment probably recognise the intent behind it.