As you know, there are ranges to all offences. There are some that are very serious and some that are less serious. The problem with minimum sentences is that they treat less serious offences the same as a more serious offence, and in doing so they discard some very important principles of our justice system.
One of those principles is rehabilitation. When you over-incarcerate someone, there can actually be an increased rate of recidivism after their release, and of course you don't want that. You don't want someone released from jail who's more likely to offend. No one wants that. Your solution, though, begs that to happen in many cases. That's when you need to take a nuanced view. You need to be dispassionate about things, look at the evidence and see what actually works—to sort of leave rhetoric aside and see what works.
If you really do want to protect the public, if you really do want to rehabilitate, and if you really do want to deter, there are ways you can do that. But unfortunately, if you don't follow the evidence, you don't accomplish that, right?