Adding on to what I said earlier and answering OP’s question, if a more efficient version of the A380 were to be developed, Emirates would jump on it.
Emirates’ recent order for a bunch of A380s(now cancelled I think?) was a final effort to save the program. They love the A380, offering service from Dubai as a transitioning hub from North America to Central Asia, Europe to CA/Asia and Australia/Oceania, and vice versa.
Now, theoretically, British Airways, based in the heavily slotted London Heathrow, can potentially order a new version of the A380. They need to maximize capacity if they are slot restrained. However, LHR is planning a 3rd runway which will add slots to the airport.
We’re seeing an existing transfer from maximum capacity to more frequencies, which is assisted by airline agreements such as Joint Ventures. With the AA/BA transatlantic joint venture, they can freely swap metal and optimize the capacity between two cities. If they think a route needs more capacity, they’ll switch aircraft. Either one or two years ago, AA/BA switched up frequencies between DFW/MIA-LHR. AA reduced MIA-LHR and let BA takeover. This past year, AA launched service on PHX-LHR using its own metal, which in turn led to BA reducing LHR-PHX from 14 to 7 weekly since they have a metal neutral agreement. Instead of possibly maximizing capacity and slots with an A380, they let their partners fly another frequency. Passengers seem to prefer more options and times to fly, anyways.
tl;dr: Emirates loves A380, partnerships allow for airlines to fly routes together and favor frequencies over capacities so passengers have more time options.