Sorry for dragging this up, but I think it's an interesting question, and might merit a little more discussion. Even if the answer doesn't change.
I suspect we would have a more capable plane and a much cheaper R&D cycle if the original spec had been for one plane, a versatile F/A capable of carrier ops. The AF would have to deal with a larger wing and beefier landing gear, but that's not so bad. The approach worked fairly well with the F-4 (some early problems there for sure, but not really due to commonality). You don't have to invent lift fans or whatever. I do wonder what it would have looked like, certainly nothing like the F-35.
On the downside, if you can't use it on small carriers, you lose the UK and most or all of the Marines purchases, and your production run gets smaller. Shortened production runs tend to annihilate military programs. Look at Zummwalt, B2, etc. Might've ended up like the A12.
The Navy, Air force and Marines have missions they need to be able to fulfill.
Government sets aside money to pay for assets that can cover that capability.
Our defense budget is X dollars and each service has to justify their chunk of change.
In order to bring unit cost down, a manufacturer needs to sell a lot of planes and engines.
F-35A is the cheapest model and has the volume. This is the aircraft that everyone and their mother will be buying.
F-35B IS the equivalent of what a dedicated VTOL \Harrier replacement would look like. The Marines need it. UK needs it. Italy and other countries that have that requirement to either deploy from kiddie carrier or deploy close to the troops runways be damned. Even Israel wants F-35bs.
F-35C is the priciest, lowest volume version for a reason. Big wing. structural crap. Stuff that needs to be put in place specifically for US navy requirements. What you seem to be proposing is that we should have only built an aircraft that met USN navy requirements.
If the starting point is the heavier, larger F-35C, then what becomes of the aircraft that satisfies the requirements of F-35B customers? A new aircraft program to replace Harriers\AV-8b's? You can't deploy an F-35c on a Helicopter carrier. You can't deploy F-35c to forward airfields like you can with Harriers.
You are now looking at 2 distinct aircraft programs now where you have not only doubled outlay for program costs, you now have higher unit prices for both "F-35" and huge unit price for "Mystery VTOL aircraft"
If we had unlimited budgets and could guarantee unlimited budgets for 60 years then it would be feasible to make dozens of specialty aircraft with narrow mission capabilities.
The F-4 was designed to be a Navy interceptor and then over time had its capability expanded. Systems were added or updated over time.
So when the program started for the F-4, they had concurrent programs and platforms other aircraft designed for singular roles.
FYI: When the F-4 was being designed, they were working on specifications for VTOL aircraft because they saw the need for that type of aircraft and saw the benefit it brings. To get rid of VTOL aircraft means you lose a lot of flexibility and capability.
We spent X dollars to develop multiple aircraft and as time went on we spent more money expanding the capability of each unique platform. It is not cheaper to pay for multiple programs and then maintain and upgrade multiple platforms over the life each distinct program.