The Ford and Nimitz class do need vast crews. However, they can maintain 4-8 times the sortie rate. They don't need refuelling, and don't need vulnerable supply ships to follow them into war. Indeed, they're so vast they carry bunker fuel themselves to resupply their escorts. Their effective time on station is much longer than the QE class.
OK, they're arguably more general purpose than Nimitz and Ford, being able to support marine expeditionary operations and humanitarian operations far better than they can, but the US have the America class carriers to fill that need. As a consequence of making them general purpose instead of attack or ASW vessels is to make them a jack of all trades, but master of none.
The Queen Elizabeth class is big, very big. The good news is that outside of the United States there isn't another navy that can match them militarily, although forthcoming generations of Chinese and Indian home grown designs seem likely to do so. They're big, they're capable, but they're not nearly as capable and effective as they could be if it weren't for repeated political meddling with costs, build, design and intended mission.
A Nimitz carrier is militarily, on its own, designed to be a match for any 2 entire countries navies. As lovely as they are ours simply aren't in that class for force projection and area defence.