ProfessionalWiki
Add "mass upload" permission
It would be nice if there was a specific right that controlled access to the special page.
There is already $wgSimpleBatchUploadMaxFilesPerBatch, which allows to set the max batch size depending on the user group. It's not quite the same as blocking access to the Special page, but the effect is similar. Also the warning is the same: This extension is using the MW Web API. Blocking the page would still allow to use the API, so this feature might deter the casual user, but should not be considered an effective measure e.g. against determined spammers.
My wiki has specific policies for formatting uploaded summaries. The goal would be to prevent new users from uploading numerous unformatted files before having the chance to learn the proper process. That configuration setting does appear to satisfy the requirement, and I'll have to test it out.