I always wondered this..it seems to me that God would have done it himself to show the oh'mighty power bestowed in him for all to see.

The scenario you're referring to is Revelation 12:7-9,

"And war broke out in heaven: Michael and his angels fought with the dragon; and the dragon and his angels fought, but they did not prevail, nor was a place found for them in heaven any longer. So the great dragon was cast out, that serpent of old, called the Devil and Satan, who deceives the whole world; he was cast to the earth, and his angels were cast out with him."

Now to answer your question, first take a look at what God said in Ezekiel 28:14-16,

"You were the anointed cherub who covers; I established you; you were on the holy mountain of God; you walked back and forth in the midst of fiery stones. You were perfect in your ways from the day you were created, till iniquity was found in you. By the abundance of your trading you became filled with violence within, and you sinned; therefore I cast you as a profane thing out of the mountain of God; and I destroyed you, O covering cherub, from the midst of the fiery stones."

Now, notice that God said "I cast you out," to answer further, the war between Michael and Satan has not occurred yet, the scripture there is an apocalyptic vision. It will happen during a time of tribulation of which no one has yet to see; in which God will display his mighty power for all to see in the form of judgment on the sin of this world (Revelation chapters 6-16).

See, as of now Satan still has access to heaven to come and go as he pleases, he does this to harass and accuse those who are right before God (Job 1:6-12). But here shortly he is going to get kicked out. Michael and his angels are going to fight and prevail against him, and he is going to be cast out for good.

I find it interesting that the name "Michael" means "Who is like God?" It's a rhetorical question because there is no equal to God; and that was Lucifer's original sin--he claimed to be equal with God. Perhaps this is God's personal way of irony towards Satan, to have Michael battle him. Notwithstanding, who are we to question why God would have Michael fight instead of himself?