In other words, it gives the US an option short of sending a CVN, and of course more ships with a fixed wing capability is useful
No, it doesn't, since the Amphibs are not deployed with organic AEW, nor is the actual Air Wing component remotely as capable.
In Re AEW: Hawkeye is not a VSTOL aircraft.
Now, if you want to "put a big ship somewhere" and you don't think any actual incoming air assets are likely to show up, sure, send LHA/LHD and a few escorts depending upon how you want the presence mission to play out. Been on a few of those.
But DON'T EVER PRETEND than a Harrier carrying amphib in the USN is a sub for a CVN plus its embarked airwing.
NOT EVEN CLOSE.
I am an American. I was a career Naval officer (aviator sort).
I find your citing "some American" of dubious understanding to be suspect.
EDIT: as to this little joke ....
Additionally, the reason the USMC wanted the Harrier back in the 70s was that it provided them with firepower only a short flying time from the shore, making up for the loss of the six inch and eight inch gun cruisers that provided naval gunfire support during the Cold War conflicts in Korea and Vietnam.
Sorta funny, given that the battleships were reactivated for Viet Nam (see USS New JErsey's fun and games there) for Lebanon (80's) and for Desert Storm. Oddly enough, that didn't put the Harriers to bed. Neither did the RAP rounds for 5", nor the proposed RAP rounds for the 16" before the monpower bill in Rummy's and Cohen's Navy coudl get you the manning of four Arleigh Brurkes for one BB.
You'll also find that, in the 1970's, the USN tried to put an 8" gun on the Spruance and hull -- it didn't work out very well. Likewise with Ticonderoga, same basic hull, and that didn't either. Don't recall if it was money or structural mods, but I think it was a bit of both.
That initiative was in fact directly related to the need for NGFS better than the 5" gun on most destroyers and then cruisers as the 6" and 8" cruisers were one by one retired. USMC continual demand for NGFS over time has, in a pure sense, remained an unfilled desire.
The Marines desire for a jet that operated at something other than a big airfield, or from a flat top, is part of their general operating philosophy of air power being a sub set of the larger battlefield funciton of "fires" but I am digressing into doctrine here.
Anyway, I find some of the mythology to be amusing, some less so.
On the other hand, who knows what soap was being sold in DC when the Harrier was proposed for a Marine Air Wing?
Lobbying for a capability results in some curious statements, like the "ring of iron" justification for more LA class SSN's to be in Direct Support of the CVBG ... and which more or less was never going to happen in practice.