After discussing this issue with garaudy.etienne@mongodb.com, I'm opening this ticket to request a backport of SERVER-6491 to older versions of Mongo, 4.4 and up if possible, considering there may be a number of customers with extensions as we go through the EOL process for these versions.

My customer was able to drop a shard key in production on Shard-0 causing a long queue of deletion tasks resulting in performance degradation. The customer eventually scaled up to allow for additional headroom for the deletions to catch up once the index was rebuilt. Additional context is available in the ticket linked. Their server version at the time was 4.4.18.