I can't force users to use reasonably long passwords. In the case that they don't (and some certainly won't), it's preferable that their password is still as good as it can be given the length.
When it comes to web logins, brute force is probably the least effective method of attack. Social engineering, dictionary attacks, rainbow tables, password lists, guessing and so on are all much bigger concerns. It's my thinking that most of those threats are better addressed by sacrificing a negligible amount of entropy and removing a large subset of weak passwords.
Moreover, this reduction in entropy only applies when the attacker knows the algorithm used to derive the password, making it even less relevant for the average case. (That's not an appeal to security through obscurity; just an observation).
>Whereas if you generate passwords of decent length and at random then they're random so there's no purpose in checking them.
Random != secure. "aaaaaaaaaa" could be the result of a random function. The goal is to create passwords that are both difficult to brute force, and difficult to guess, while making no assumptions about the length.
Entropy has diminishing returns; if it takes 10 million years to crack a password, another 5 million doesn't increase security. However I would re-consider if someone could provide a concrete example of how the small loss in entropy could lead to a practical vulnerability.