Off topic:Why adding adapter first and probe later, but not the opposite?

Question

[CY]

I saw it is common to add adapter first and then use probe to grep interested fragments in lots of NGS protocol.

I am wonder why don't we do the opposite? Would't that be more efficient since that way we can only target fragments being bind with probes and don't have to waste adapters on unwanted fragments? Is there any technical reason that make the protocol the way it is? Any comments are appreciate!