In my experience, you are correct about the Pacific. USA just needs to spend enough there to keep Japan from taking Hawaii or Sydney.
On the Europe side, Germany shouldn’t be able to take London on turn 2 ever unless the UK player just abandons it. To even have a chance, Germany would have to build all transports on turn 1, and then UK could just easily build max infantry in London, not move any units out, move the Scotland units in and Germany would have little or no chance of taking it.
In the Mediterranean, usually the UK destroys most of Italy’s fleet before Italy has a chance to use it. Sometimes they get lucky and are able to destroy the rest of the UK fleet on their turn, but usually it seems to require Germany to help finish off the UK fleet.
Generally though, yes, if the USA is unwise and ineffective, then the Allies will usually lose. If they invest nothing in either the Pacific or Europe sides, the Axis should be able to win fairly easily on that side most of the time.