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.