I'm not sure why it is so difficult to believe.
Up to 2017 China has operated Liaoning for five years, and 071 LPDs for a decade.
The USN's first LHA class was the Tarawa class, which was their first helicopter carrier with a welldeck. Before that they operated the Iwo Jima class LPH which along with a few converted Essex class carriers were more helicopter carriers than LHA or LHD.
Great post.
And as far as actual designation goes...that is correct. But as you say, before the Tarawa Class the US had built the first full class of large Amphibious assault ships that were designed to be such from the keel up, which you called. And they were the Iwo Jima class.
They were designed for large scale US Marine assault from the sea and from the air...but they did not (as you say) have a well deck and were thus called LPHs. Their full load displacement was about 20,000 tons and the US Navy built seven of them from 1959 to 1968 before going on to the Tarawa class.
They found that the old way of loading landing craft either with cranes and then by nets over the side was just too slow...and thus the well deck came into being for the Tarawa class, and the Iwo Jima class became pretty much pure air assault vessels.
By then the US Navy had other well deck ships in the LSD classes too.
Here's a good look at one of the Iwo Jima Class:
But the US Navy and Royal NAvy had well deck ships, with smaller helo decks in the 1950s. These ultimately developed into the current Whidbey Island class LSDs, and the ultimate San Antonio Class LPDs.
Now the new LSDs will be the same hull as the San Anotnio class and the US will build twelve of those...ultimately having 24 hulls of the San Antonio class tpe vessel, with the San Antonios being heavier and having more command capability and better air assault capability.
The new LSDs will use the same hull, but be klighter and not quite as versatile.
But having them both be the same hull will do two things
1) Make them easier to build than an all up new design.
2) MAke them easier to maintain and operate.
3) Give the US Navy a larger LSD design than they have had in the past...but they will not carry as many LCACs...at least I do not believe they will. They would have to extend the well deck significantly to do that and I just do not think that is going to be the plan.
So, ultimately the US Navy will have 10-12 LHD/LHAs, 12 LPDs, and 12 LSDs to be have 12 full ARGs, with six or seven available at all times, and up to nine perhaps in a full surge need.