Think about the size of the armada and the various types of ships used when the Allies invaded the continent at D-DAY. They used about every type of amphibious design.
But take a look at what types of amphibs they had available.
They had landing crafts of various sizes and they had transports for the infantry because the infantry landing crafts didn't have the seakeaping to make the trip.
Not a single LPH or LPD in sight.
Airlift is limited a space/weight availability per platform.
You would need a lot of the huge Me 323 "Giant" gliders or their multi-engine counterparts to move artillery & armor to the UK.
Yes? That's not going to change if you fly from an LPH. The allies did very well without suspiciously modern transports.
Why limit youself to a single method of delivering troops & resources.
Economy and capacity.
You'll get more capacity and flexibility from using several civilian transports rather than a few military ones, and it'll in all likelihood
Make the defenders life as difficult as possible.
SOmething which is better achieved by landing better equipped troops via conventional means. (All the money that you don't spend on LPD's etc. can be used on improving your troops equipment.)
You're trying to wage a 1940ies war with 1960ies or even 70ies technology, and you're doing it with a fleet better suited for the Pacific than the English Channel
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That which does not kill me has made a grave tactical error
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