There was a recent commit for a similar performance problem, which will appear in 9.6.10. But that was specifically for cases where there were multiple dropped tables per transaction, and large shared_buffers.
I can't reproduce your single-drop-per-transaction problem. The replica has no problem keeping up with the master.
Can you share the reproduction scripts, and any non-default config settings? Especially the setting of shared_buffers (on both master and replica, if different)
Cheers,
Jeff