You didn't answer; but maybe the question needs to be clearer. Okay, we don't build carriers based on what China builds.
That said, how many "hot spots' do we need to be able to cover at the same time? As YOU point out, a carrier can do X,Y,Z in one place and then a week later do A,B,C 5000 miles away. Actually, that math is about right. Nuke carriers can travel at about 30 knots or over 750 miles/day. So in a week they CAN be 5000 miles away.
So, now it boils down to how many places do you think we should be able to park carriers at the same time. Multiply by three and that's what we need. As it stands, by YOUR math, we can cover four places at once. Now THAT'S gotta be enough. If not, then we're either at war or we're really paranoid.
And stop lecturing us as to what a carrier is and what it can do. Jeez, carrier dominance was established in WWII at Midway. It was the end of the battleship. In the space of a few hours, the US had established virtual maritime dominance in the Pacific.
But, to the issue at hand, we have a carrier near Iran and one near Venezuela. So we're well equipped to handle that obligation. And that includes maintenance, shore leave, etc, etc. So the USS G. Ford has been at it for about 8 months. Why can't we swap it out for any one of the other 11 ships? This doesn't seem like a problem with adequate materiel; but one one of logistics. And it sounds like a few of the 5000 crew members ought to learn plumbing. And missing the funeral of a great-grandfather, sad as it sounds, just seems like snowflake whining. Write a letter to "Warrior Hegseth" and see what he has to say.
I have great respect for the military. They do a job that's necessary and one that I wouldn't do. But service members know what they signed up for. Hardships are part of the deal. When I was an ER doc, I worked 12 hour shifts and plenty of weekends. I missed this/that/the other family events. But it was part of the deal. I could have opted for a second career earlier (perhaps). When wound care presented itself as an opportunity, I pretty much leapt at the chance. Glad I did.