All of the value calculation aside (which isn’t news), my main apprehension about trading a UK BB for a US CR is the fact that it’s editing the setup of the board. Whether or not it’s more useful is pretty clear: In most every situation, the US cruiser would probably be the better unit on the board for the Allies. (An example situation where it would likely not be would be one of those weird games where the UK does not do Taranto, for instance.) I am loathe to discuss specific houserules on this board.
And speaking of killing the UK BB not being worth the US making +20 income, have you forgotten the part where you also kill 24 IPCs of mobile American units on the Philippines, one of which is a fighter?
I clearly assign more practical value to the British BB than you do, and maybe that’s wrong, but here’s some words on that:
It can suicide into something of Japan’s with ANZAC coming in for a second hit as early as the second round (but usually the 3rd or 4th). If they’re a bit lucky (and they don’t really need to be depending on what you do), this can damage a carrier, putting two planes out of place (or destroy them outright), or kill a transport and strand some ground units, or whatever else. The threat of doing this is enough to alter the aggression level of Japan throughout play. I probably don’t need to mention “fleet in being” to you. I also agree that it’s worth destroying the hell out of that British battleship at horrible UK nominal value:JP nominal value ratios if it means damaging carriers or otherwise weakening the Japanese fleet in a timely fashion when America is showing up. As Japan, removing this variable is, to me, worth the 2/3 chance of losing my cruiser.
The main problem I’d have of convincing you of the BB’s worth, I think, is the fact that after the first one or two rounds of the game, naming every situation that could arise where the BB (or any other unit for that mater) could possibly be useful is nearly impossible, and nobody would want to write or read a ten page forum post of nested if statements anyway. One example is if your Indian cruiser heads west to hit Ethiopia, then doesn’t immediately turn around (say, to hit Iraq, or to go into the med, or whatever else), the BB can also be necessary on UK 3 to block a J4 hit on Calcutta if you’ve slightly overextended your ground forces in southeast Asia (for what is presumably a good reason).
As far as the cruiser’s worth to Japan:
Japan begins play with four boats, and will likely never build another, that can bombard. I rarely, rarely find myself needing more than two of those bombardments in a game, possible exceptions being hitting Calcutta or a US Korea full of slavic meat shields. Or hell, maybe Cairo. Yes, it is a slightly souped up destroyer in addition to this bombardment, I’ll give you that, but I don’t really feel like the loss of this 50% chance to kill one unit on the first round of combat, only when I’m landing 4+ units, to be a big loss. Additionally, and especially because of, Japan’s having enough air power to seal the deal in the first round of the majority of its fights where the bombardment would be most useful is nearly always enough. (One exception is taking two territories 3 spaces off a naval base where planes can’t follow, then you might be able to use all four of your bombarding ships. This is definitely not a common occurrence.)