You could, but they usually find a way round it.
It also stops you from observing the evolution that always takes place.
Blocking, counterintuitively, maintains a relationship. The block becomes a permanent wall.
Blocking is also a reaction. You've let them know they've annoyed you. They get a payoff, because it means they're important enough to warrant being blocked. It actually rewards the behaviour.
It also tells them something about you. It tells them that they got your goat. They don't need to have that information.
'Honey, he cain't get your goat if he don't know where it's tied.' (Al-Anon saying from West Texas)
Instead, I either ignore completely or mute and/or archive (in WhatsApp).
This allows the incoming communications to disappear into the void.
No reaction. No disclosure of information. Nothing. If it doesn't merit a response, don't give one.
The other person's contribution to the situation evolves, and they will sometimes go through different stage: insistence, pestering, threat, accusation, jibe, manipulation, invocation of pity, babbling, you name it.
But it always burns itself out.
It takes two to tango, and blocking is a tango move.
I stay off the dance floor.