You're looking at a three-way tradeoff.
To get the fastest speed and the lowest risk will usually cost you the most. In my experience, most CEOs and CFOs want to maximize speed and minimize cost. It takes a while to get them to appreciate the cost of accepting the risks that go along with maximizing speed and minimizing cost.
On the other hand, DBAs tend to want to minimize risk.
If you store the database and its backups on the same server, then whatever might destroy the server might also destroy your backups. That's usually not an acceptable risk, but it's application-dependent. It takes a fairly big event to destroy a server; I don't think I've ever seen one destroyed.
If you store a database and its backups on the same physical disk, then whatever might destroy the disk might destroy both the database and your backups. I've seen disks destroyed quite a few times. This is almost always an unacceptable risk.
Some speed issues can be mitigated with solid-state disks, but these come with different costs and with some new risks.
Personally, I wouldn't like to keep backups on the same server as the database, but I might be willing to write the backups to the same server (anticipating high speed and low cost), and copy or move them somewhere else later.