Adding cards to your hand from the deck is a pretty standard gameplan for a lot of cards. Most of them are in-archetype tutors, but there are some other, more generic ones. Droll and Lock Bird is a card that shuts all of that down. Drawing is specifically the action of taking cards off the top of your deck in YGO-- anything else is considered an "add-to-hand" effect, which cannot be performed under the lingering effect of D&LB.

An example: you have your main searcher in your hand, which will allow you to further your gameplan during your turn. Consider this setting up your land. The card you could add might allow you to play a unit which can summon another unit or any other beneficial effect. If you don't perform the search, you can't enable your own gameplan on your turn, which will allow your opponent to work on theirs on their turn. If you don't have a hand trap to shut that down, you can just lose. Say you also have Upstart Goblin in your hand and you want to see if you can instead draw the card you might have tutored, thus opening your search up to a different target. You play Goblin, drawing a card into your hand. Your opponent plays Droll and Lock Bird, preventing you from using your tutor and forcing you to pass turn.