At a former job I managed backups for over 300 SQL Servers, and all of them were backed up to UNC locations on file servers dedicated to SQL Server backups. We did daily full backups and transaction log backups every 15 minutes for all production databases (4000+). We had only had occasional backup failures, and they were mostly transaction log backups that run OK on the next 15 cycle.

As long as the file servers and SQL Server have good network bandwidth, and the disk arrays on the file servers have enough speed to support the backups, you should be OK. Don't make the mistake of thinking that you can skimp on network and disk speed.

Backups to a UNC location are usually a little slower, but we were backing up some databases that were over 1 TB in size with no problem. I recommend that you use backup compression whenever possible to speed up the backups.