You quote Veeam's own text, which at no point uses the phrase media server. If you're going to educate people at least use the correct terminology. The correct term you're looking for is Repository.
"Based on common industry parlance, the target-side Veeam Data Mover Service is referred to as a media server."
Not sure you can call a single service a server. A service, well lots of services actually, typically run on a server.
"However, while this might have been sufficient in an earlier generation, today’s RTOs and RPOs demand an application to be up and running from a fine-grained restore without the application user having to browse files and stitch things together."
Oh you mean like SQL database restores? https://helpcenter.veeam.com/backup/howtosql/how2_sql_restore_with_vesql.html
Restore database to the original or different location, to the state as in the selected restore point of SQL Server VM.
Restore database to the selected point in time.
Restore database to the state prior to undesired transaction table
I'll rescind the final statement, having read it again.