I am confused, why do you single out minion generals? Everyone gets gold at the same rate. Are you insinuating that assassins get more gold because they can kill creeps faster? Or perhaps because you think assassins kill players and get free gold?
As the QoT your default attack is an AOE. You should always lead the game in creep kills. This does equate to more income, but not as much as if you were to go around killing other players. And by default attack I mean when you are in the bulb. If you find yourself out of the bulb, go back in, you are doing it wrong.
In addition, your shamblers attack in a very long straight line, damaging anyone in the path. Position your minions to take advantage of that. It's necessary.
Lastly, your job early game is to never die. If you die, you are giving the assassins the game. Assassins cannot compete with the amount of minions a general can lead around at end game. They have to get you early and get you often, otherwise you both end up with the same income, the only difference is that your income can create more minions that do more damage and require more attention to kill, where as they get some crappy items that, in the end, don't matter.
No other general has the ability to take out a wave of creeps like the QoT. The only other classes that can get close are the Torch Bearer and possibly Rook. But both of them have to spend mana on what you can do with general attacks. Shoot yourself if you ever find yourself wasting mana to take out a wave of creeps.