Is omnipotence in and of it's self a logically impossible paradox?

Many people have argued that an omnipotent god can not exist as omnipotence is a paradox. The most famous argument in favour of this idea is probably the paradox of the stone, “can god create a stone so heavy that not even he can lift it?” however, this argument does not hold water as the question is fundamentally flawed, and actually a little deceptive.

The question is flawed because of what it does. What it does, is it takes omnipotence and disguises it as a task, in this case, creating a heavy rock. It then takes the very same omnipotence, and disguises it as a different task, namely lifting the rock. So the question is basically asking, can god be so omnipotent that not even he can be more omnipotent. No matter how much he tries to lift the rock he already has all of his power working against him. Its like asking can a chef cook a meal that is so tasty that it tastes better than his tastiest dish, its a nonsense question.

You can create some paradox, but you need to bring omniscience and/or omnipresence to the table in order to do so. (at least how I see it) for example, “can god leave a place? If he can he is not omnipresent and if he cant he is not omnipotent” or “can god solve a mystery? If he can he is not omniscient and if he cant he is not omnipotent” there are hundreds of such examples, but none that I can find that show a paradox utilizing just omnipotence.

So, is omnipotence in and of its self a paradox?