At the moment the only known efficient way to get a system-wide table count for a mongod instance is to walk each of the databases and each of the collections getting a count of the total items.
Why this matters:
Our scalability issues, because of our structure, are entirely based on number of files. As we approach ~350,000 collections + indexes, we begin to experience numerous issues. So we run multiple instances per system of mongo, split on various ports, in order to keep that number down, yet properly utilize our Optane drives and memory.
Our solution to tracking this information systematically has been to have a tool that connects to each database, walks each db and counts the tables. We then report this back into a metrics database. We prioritize the creation of new dbs and new instances of mongo based on how many files. We've found the best mid-line to be the ~100k file range.
Running the above query is somewhat expensive and causes unnecessary utilization, and may load unneeded data into memory. I believe wiredTiger, internally, tracks its open tables and would be able to report this number (even if only an estimate) in its statistics.