Yes we do - and many of our Business Customers are doing exactly this.
Some of the advantages are that you will have full physical control over files being sent, and it will usually mean faster transfer speeds as well (depending on internal vs. external usage).
The requirements are:
Windows 2008 R2 or Windows 2012 - with all Windows Updates installed
Enough storage space
2 GB RAM
Minimum 2 cores
We need full local administrator access - and we'll take full control/responsibility of this server. This means performing maintenance, Windows updates etc.
It does not need to be a part of your Windows Domain
Network Access - HTTP/HTTPS
Network Access - SNMP (from our IP) so that we can monitor the server continuously and make sure it's working as it should. We will get notified by SMS/Email when something is wrong - and fix it asap
Network Access - RDP - (from our IP)
One time setup cost for internal fileserver: $5000
Annual cost for updating, monitoring and handling an internal file server: $5000
Installation time: Within 24 hrs (at most) after we get server access.