Any time someone overanalyzes Friends, I always come back to this:
It's a sitcom.
It's primarily supposed to make you laugh. It's not a drama. Characters' traits bend to the will of the writers' jokes.
Joey accidentally proposed because it was funny. Rachel said yes because it set up more jokes. Joey didn't clarify that he wasn't proposing because, again, this was all intended to set up more jokes.
You tend to get ridiculous plot premises in a sitcom when the couple that are "supposed" to be together get together too soon. It's more interesting to have the tension of them being separated than it is to have a happily married couple that are perfect for each other. And it's easier to make jokes.
In an alternate universe, Joey clarifies he wasn't proposing immediately, Ross proposes, and they live happily ever after. But that's not funny, so that's not what we got.