A repost of my earlier comments seems to be in order...
What seems to be missing is the fact that the ignition switch has two circuits, Run & Accessory. The Accessory circuit is NOT powered on when you turn the key to the start postion. This reduces the electrical load on the battery. Ever notice that the stock radio goes off when you crank the engine? That's why.
If you use a push button, you will have defeated all the safety interlocks and allowed the accessories to draw power when you crank the engine. Not a good plan, especially when it is a cold winter day and your battery is a little on the tired side.