A faster ascent does take less energy - not because the gravity is stronger at lower altitude (the difference is pretty minor) but because the rocket spends more time fighting gravity. Think about the extreme case where the rocket is barely moving up - it will use up all fuel before it gets to any meaningful altitude. It's kind of like walking up a downward escalator - you have to expend energy just to stay in one place, and it's actually easier to run up quickly. Once you're at the top (in orbit), you can stay there without using any energy.

But there are limits on how quickly a rocket can accelerate, such as:

• Quick acceleration requires more powerful engines. The engines themselves get heavier. This is mainly an issue with liquid-fuel rockets; solid fuel rockets don't really have an "engine" and you could design it to burn all the fuel very quickly if you want to.
• The quicker you accelerate, the more G force & vibration the payload experiences. This is especially a problem if the "payload" is people.
• If you accelerate hard, you end up traveling very fast through the dense low-altitude atmosphere, which means a lot of mechanical stress & vibration on the rocket.