Because the method is indeed async, you can say "I'm fine thanks how are you" with no future expectation of immediate reply. It's okay. If they wanted sync, they would've asked for a phone call.
But, suppose you switch to sync. They ask a question. It indeed isn't important to you right now. Tell them you're busy with other tasks, and you'll reply later. It isn't rude, we all frequently work with others that have a lot on their plate.
I agree with you, but if you find yourself feeling burdened, perhaps there's a genuine opportunity for introspection: why are you feeling burdened? You don't owe them anything, they're asking you for your time. You're doing them the favor; you're under no obligation. Feeling burdened seems self-imposed.
It can be sometimes easier to shift your own perspective than it is to change the behavior of others.
Because humans have not adapted to online, emotionless, body language-less chat, and it's cumbersome and unnecessary to emulate this behavior. It's burdening the same way I have to smile and say thanks to the pizza delivery guy instead of slamming the door in his face.
But, suppose you switch to sync. They ask a question. It indeed isn't important to you right now. Tell them you're busy with other tasks, and you'll reply later. It isn't rude, we all frequently work with others that have a lot on their plate.