As a general rule, the higher you go up on your toes (well, really, the ball of the foot unless you're doing ballet), the more you reduce stability and power, but conversely you gain a bit in height/distance and increased flexibility/mobility. If that inch makes the difference between hitting your opponent or not (particularly if they've opted to try to just dodge out of the way without raising their hands), it may very well be worthwhile to hit a little bit softer just so that you can hit. And if your ankles or knees aren't flexible enough to complete a kick, going up on the ball of your foot, even lifting the heel half an inch, makes pivoting easier, which may protect your joints on hits or misses.
One possible exception (which I don't think is what you're going for, is when you're on the ball of the foot because you're getting a little bit of extra distance/bracing kicking forward, like stepping into a hard front push kick so that your bracing foot is behind you and your hips and torso are driving forward with the kick.
One caveat to that is that you should keep your weight on your foot. A bad habit to fall into when going up on the ball of your foot is letting that momentum lift you up, which greatly reduces stability and increases the chance of being swept or otherwise knocked down.
Lastly, in some styles, the instability can be useful, particularly if competitors are not allowed to strike a downed opponent. I know Tae Kwan Do is a frequent whipping boy here, but their rules at one point incentivized kicking and then falling because it prevented counter-attacks.