vagabundo
Adventurer
All of the above are valid points that I agree with. My issue is with the perceived achievement of killing a minion. AC and tactical advantage aside, killing a monster with lots of hit points has a great deal more kudos than killing a monster with one hit point. I do not find killing minions satisfying.
The simple solution is not to use them. They are a tool for the DM and you should ask yours not to include them or up their HPs to something like 3*level.
You can replace every four minions with a non-minion monster of the same level.