actually, you are entirely on the “kill 3 inf”
first off all, you are assuming the axis will defend weakly, on the shores. many axis wont do that, secondly you are assuming that you could not get the same result by adding planes, and the planes would gain something by not helping.
an eksample would be
invading with 2 inf against 1 inf, with 2 Cr, against 1 inf, your average losses is 1.5 ipc
invading 2 inf against 1 inf with 2 ftr support, you take 1.3 IPC in losses
the inf you have left, will attack defend and kill about 1.5 IPC on defence.
most axis players will deny you the advantage of doing microinvasions agains weak stacks.
I am not assuming the axis is weak defending! Thats the point. You won’t attack a stack you are likely to loose against with air, but you can with crusier bombardment. UK does not really need 2 additional infantry, but needs to distract Germany from solely focusing on the USSR. So attack a Stack of ANY size with 2 Inf and 2 Crusier bombardment. You have a reasonable chance to inflict 2 losses by shore bombardment for the loss of two infantry. Every plane you would have sent would be lost. Thats my point.
To get to your point:
invading with 2 infantry against 10 Infantry would economically be prefareable with crusier bombardment and not by sending in planes. Thats what I wanted to say.
At last: Infantry and fighter are the most valuable pieces in play. Best Bang for the Buck. But if you need to add to your fleet and you are thinking about a destroyer, just keep in mind, if you are planing to start a lot of amphibious assaults it just needs 4 landings until the crusier (1) will give you a benefit.
@Kreuzfeld: As far as I read this discussion, we were discussing by comparing crusier to destroyer or submarines, not to planes. Planes are always the better by than ships.