If you have two solutions and the first solution requires humans behave in a certain manner (getting them to use high entropy passwords) and the second does not. The second is more secure.
The method you purpose is less secure as humans often use low entropy passwords even when you ask them not to. If you are building a system only for humans that use high entropy passwords (are you really willing to bet the farm on that just to save a couple clock cycles) or other machines it might work but I also see no benefit to that approach so you might as well just bcrypt it and call it a day anyway.
I proposed no method. I simply made the statement that typical cryptographic hash functions are optimal (and better than the alternatives) for high entropy passwords. I said nothing regarding low-entropy passwords.