I think you meant dh_conn_ref and dh_conn_handles - I agree that those count the items listed in this ticket. However I believe there are two problems with this. The use of db_conn_ref is incorrect. It was incorrectly changed when sweep was split into two parts with this changeset https://github.com/wiredtiger/wiredtiger/commit/269e847ad64dd12dfcadb58f84f905069e5b8dce.
The purpose of db_conn_ref is to count the times that we find an idle handle and after we lock it we discover the handle became referenced and used again. I think that may also have motivated your suggestion about the name. The name is okay in the proper usage and context.
Therefore, once that fix is made there will not be a statistic that indicates the number of time we remove a dhandle from the hash list. The dh_conn_handles does count the number of handles we close. I will fix those two things.