IIRC, most fighter bombers used impact bombs. Delayed fuse bombs were used mainly to attack buildings and sometimes ships. It's not a case of them being short in supply, just not suitable for the mission purpose. After all, plenty of delayed action fuse bombs were dropped on Britain during the Blitz, as well as the butterfly bombs which could be fitted with three different type of fuse, an impact fuse, a clockwork fuse which could be set from anywhere between five to thirty minutes after impact, or the anti-handling fuse which would detonate if it was moved after impact, it was a nasty little bastard and first used against Ipswich, which isn't that far from where I live now
Naturally, it was a tactic employed by both sides, I have no doubt that Bomber Command dropped their own delayed fuse bombs and mines on Germany.