If the attack on USS Liberty was intentional, what would have even be the purpose of such an attack?

It sounds like a horrible way to get support and if they just wanted the ship out of their waters they had way better ways to go about it. Anything that seems to work are based on unsubstantiated conspiracy theories that would need to be true, and even then would not make too much sense.

I just cannot think of a good reason why Israel (or literally anyone for that matter) would purposefully attack American naval vessels if they didn't explicitly want to start a war with America. At that point, a simple appalling level of incompetence makes more sense to me, especially looking at other cases like the Dogger Bank incident, with the cover up being to conceal just how bad the incompetence was.