Shipbucket

Not if you want it to perform the same mission as the current carriers. First of all if you want the UAVs to take over the role of manned aircraft then they'll need the same performance as the aircraft they're replacing. As a result it wouldn't be any smaller, any cheaper or any less maintenance intensive. There's a reason why UAVs are still restricted to surveillance and COIN roles.
As a result you'll need a carrier about the same size as the current one to deploy the same number of aircraft. A fully loaded Nimitz has an aircrew in the vicinity of 250 people at most. Ad some catering and service personnel and you could conceivably remove three hundred people from the crew. Of course a lot of those people will be replaced by additional technicians and maybe a few pilots to remote control the UAVs just in case. What you won't see is a reduction in mechanics and deck personnel. Remember, we're dealing with fast jets here and until you come up with a robotic mechanic you'll still need brown shirts, red shirts, purple shirts, yellow shirts and white shirts.
In conclusion, as long as the US Government wants the navy to be able to do what it does now an all UAV force won't confer anywhere near the amount of savings people talk about.
The problem is that with the exception of a few high altitude recce birds UAVs have by and large replaced low-end aircraft were crew cost is a major factor. Once you get into fast jets the pilots wages becomes peanuts compared to all the other operating costs.

Then why build more when we have more than enough?

I am not green to the point that I would suggest that the US Navy build such vessels, hell I'm actually against the construction of nuclear carriers because they're TOO BIG AND EXPENSIVE! (we should revert to small carriers and UAVs, that would be more than enough and save us billions.)