That's exactly how I kick, it's not push kick at all, it snap forward and hit with the ball of the foot to dig into the target.
This is a much harder kick than push kick, but do it right, it's the highest speed that dig into the target. But it's hard, all these years practicing( not hours a week, but consistent throughout the years), it's still hard to kill to the solarplex without sliding up the bag and lost the power. Also, sometimes, the ankle of the foot is not tighten at the moment of contact and give, that reduces the power of the kick.
It's the timing, your foot should be relax when starting the kick, then when the ball of the foot almost hit the target, the ankle needs to tighten up so it doesn't give at the moment of contact. Just like punching, the whole arm should be relaxed, then throw the punch, the last moment before contact, you tighten up the wrist and squeeze the hand to dig into the target. It just much harder to control the foot. That's what I was talking all along that a good front kick is very hard even thought it sounds the easiest of all kicks.
Actually a good push kick is not bad, it's a combination of snapping and use the hip to push forward. That's NOT a lot of non experts do, they literally pick up the foot and push forward to the object. There is no penetrating power, just push the object back. When they kick the kicking bag, there's almost no or very light sound because there is no speed in the contact, just push the bag. There's no stopping power, the opponent just get push back a step and move forward again!!!