Of course users should:
1) Have a 15+ character password.
A hashing calculation: at one billion hash comparisons a second, a 15 character alphanumeric password will take roughly 7000000 years to compare all combinations.
Aren't you reducing your key space then? Making it less secure.
No, running the result through the hash function again is a very common way to make it safer.
What you basically do is, if they can figure it out, is force them to do multiple hashes for every comparison. This is a direct counter to brute-force attacks.
If they have to spend one second for EVERY combination comparison, then it will be basically impossible for them to brute-force anything.
There are even specific algorithm which are designed just for this.
If you take the above calculation, if they can only do one comparison per second instead of a billion, then it will take 7000000000000000 years instead to test all combinations for one password.