Right, so you just want Hasten to be a pick that doesn't influence the maximum number of power pools available? Great, we got there in the end didn't we?
But even if that's the case, there's a cost to picking pool powers, which @Greycat put rather well. You're not just picking a new power, you're 'locking in' a pool, that's the sacrifice you need to make when considering builds like this. Hasten is popular, sure, so is Tough, and Combat Jumping, should they be made freely accessible outside of pools too? How far do we go with this? Do we just remove the concept of power pools entirely?
These restrictions exist for a reason, to ensure you can't just hoard all the best powers from each pool and play an absolutely monster of a build, deal with it.