Once you have played a few more games I think you will come to realize that invasions are both too easy, as you say, but also too difficult. The easy part about them is:
1. Landing Ships are, IMHO, still too cheap. They used to only cost 15 production but the cost was raised to 25.
2. No planning is required. If you see that your opponent has left a port vacant or left an air unit by itself too near a beach, you just load up any division within range and away you go. Of course, historically even commando raids required weeks of planning.
So, IMHO, if you want to make invasions more difficult increase the cost of LSs and require some sort of planning (similar perhaps to what is done in War in the Wets).
But it can also be very hard to successfully invade a well defended coastline and capture a port. If the Allied (and Axis) player is limited to only invading with a limited number of corps (say 3) then good luck invading France in 44. One way to make invading a defended coastline easier would be to allow players to build Mulberries, at considerable cost of course.
In any event, there is a limit to how many units you can invade with as as each time you load a unit onto a transport it consumes some of that nations transport capacity. So you could only have 10 large corps on transports in Gibraltar if you have a 300 transport capacity.
Yes, I basically agree with you. I've played enough to learn the hard way how difficult it is to invade a well defended Italian/French coastline, and my suggestion above isn't aimed at making that any harder.
My suggestion that units sitting in transports should require supply and shouldn't gain readiness wouldn't affect a cross channel invasion as the UK has unlimited supply, and enough ports that an invasion force wouldn't need to be in ships for more than a turn.
I'm interested in addressing the ease in which invasions can be tossed around like confetti, and one of the issues is that you can have large amounts of units sitting around in ships waiting to pounce, and that these units are gaining readiness, gaining reinforcement and upgrading, without requiring any supply. As well as helping enable off-the-cuff invasions, this as leads to gamey exploits: let's say I have reached port supply capacity in the Middle East. Never mind, put a couple of damaged units in ships, they come off the supply grid while miraculously repairing, upgrading, and refreshing in the ships. Rotate and repeat.
"In any event, there is a limit to how many units you can invade with as as each time you load a unit onto a transport it consumes some of that nations transport capacity. So you could only have 10 large corps on transports in Gibraltar if you have a 300 transport capacity."
The USA has 240 transport capacity in 1939, easily above 300 by 1942.
So yes I agree that big invasions against well defended coasts shouldn't be made any harder (in fact, given complete air and naval supremacy they should be made slightly easier.)
But I don't think my suggestion would make cross channel invasions/Italian invasions significantly more difficult.
I like the idea of mulberry option. Also the idea that a unit would have to be put into prep mode for a turn before sailing (and after this, if they don't sail, they should start to lose readiness, as per OP)
My question to you: are you happy that units in transports can repair/upgrade and gain supply level and readiness for unlimited time without requiring any supplies?