Why do we need three different versions of the F-35?

What are the service requirements that are driving these three versions?

The Air Force's F-35A is the least expensive version and it requires
F/A-22s to clear the way so the Air Force needs runways anyway. Because
the Air Force always needs permission slips to operate they can't assume
that their bases will be in the country next door so they need more
range than the F-35B offers.

The Navy needs a F-35C that won't break up during a high speed carrier
landing and they need greater range because they don't have these
"deals" with tanker builders like the AF does so they'll have to rely on
Super Hornet tankers.

The Marines are desperate to get their airpower on the ground as quickly
as possible in case the Navy pulls another Leyte Gulf on them and so
they're willing to accept a half-sized bombload on the S/VTOL F-35B.

-HJC