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

[UniCornal]

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!

[HESmith]

Adapter ligation is a concentration-dependent reaction. If enrichment is performed first, then the amount of one of the reactants (fragments) becomes low, which reduces the efficiency of the reaction (i.e., less library).

P.S. - It's not necessary to post the same question in multiple topic areas.