They don't exist, and there's no time to develop them. Remember the Hoods are only laid down to counter German BCs with suspected 15.2 inch guns. Of course there are only 3 18" inch Mark 1s, hence the 15" armament on Hood. If you're building a 1920s battlecruiser/fast battleship go with the G3s, they're far superior.
Right. And once the
Mackensens went away, so did much of the motive for the
Admirals.
Perhaps one WNT compromise could be to allow each of the three powers to have two capital ships up to 45K or 50K tons displacement (France and Italy might be permitted one each). Britain has
Hood; she could build a G3 for the other - or she can scrap
Hood, and build two G3's. The latter would be, in line with your observation, the better move (the G3 being well superior to any possible
Admiral ship); but the penny-pinchers in Whitehall will opt to keep
Hood. America and Japan would obviously complete two
Lexingtons and
Amagis, respectively. This might or might not butterfly away the
NelRods.
Still not a good move, though. The
Lexingtons ended up having more value to the U.S. as fleet carriers than as battlecruisers, just as
Akagi,
Courageous and
Glorious did for Japan and the UK. You can upgrade naval aircraft far more easily than you can battlecruisers. The US and Japan will eventually build keel-up carriers to supply the deficit, but that will happen later, they'll be smaller, and the learning curve in carrier ops will be pushed out.