If you're talking about the case where a local database forwards a read to the 'leader', and that read is put on the leader's log, but that read is only served when the read is replicated in the log back to the original local database then: It's actually less about the the leader caring about the read, and more about creating a point in time that the read will happen.

The database is using the read in the log as the point-in-time where that read happened. The writes before that point will be viewed by the read, and the writes after won't be.

By sending the read to the leader, when we receive that read back, we know for sure that all the writes that should have been replicated to our local copy have been replicated (because our read has made the full round-trip that all our writes would have, so we're guaranteed to have received all the writes before that read's "point-in-time").