Bans can be two-way here.
One can be caused by local node requesting blocks from other nodes, but other nodes don’t have them (pruned already), thus reputation will be decreased for those peers until it reaches the floor, at which point peer will be banned.
The other happens in the opposite direction when local node requests the same blocks over and over again without getting desired response. Asking for the same blocks many times will result in reputation decrease down to being banned by other peers.
So one way or another node will either sync or get banned and probability of sync decreases over time as more nodes are pruned.