Can someone knowledgeable say why drunkeness would.cause inability to speak while all other bodily functions work?

Prolonged heavy drinking, or prolonged binge drinking, can result in permanent damage to the brain and nervous system. Too, there is a disorder called Selective Mutism. Selective mutism is a severe anxiety disorder where a person is unable to speak in certain social situations, such as with classmates at school or to relatives they do not see very often. A child or adult with selective mutism does not refuse or choose not to speak at certain times, they're literally unable to speak.

Drunkenness affects different people differently...I actually get more talkative when drunk.
Generally I can talk and speak without much slurring or blurred vision, but find it more difficult to control other bodily movements (walking and picking up things can become iffy).

Lol I'm no expert but when you're drunk, you're balance is like that of a toddler learning to walk. It's normal to have the slurred speech to go with it! 😁

*bodily* XD