I won't get into the amphib V/STOL argument right now (there are valid arguments on both sides, although in an era of fiscal austerity I have serious issues with paying for a "nice to have" capability for the navy's army's air force when other services are cutting their core capabilities especially when we aren't going to deploy an ESG into a region where it faces an air threat without a big deck CSG to provide overwatch), but if we're going to have an honest conversation about the land side of this we need to define "austere" base. As the OP identified, the main LIMFAC for austere bases is logistics, to include maintenance support. Do we as a military have a need to operate out of extremely austere bases? Absolutely, and we have the logistical ability to support operations from these bases (within reason) provided they possess a runway large enough to get a C-130 in and out (assuming the base is forward enough that we don't have reliable, secure, and regular surface transport for stuff like fuel and ammo). Of course, this raises the obvious question of, "If we can get a C-130 in and out why do we need V/STOL strike aircraft?" There is "austere base with limited available support that can support conventional fixed wing operations," and then there is the definition of "austere" that V/STOL proponents use, which refers to operating out of locations that are only capable of supporting V/STOL ops. Harriers have operated in combat out of austere bases that nominally couldn't support conventional fighters (more on this in the next paragraph) but the reality is that these were more or less publicity stunts to attempt to demonstrate V/STOL's relevance.
During Desert Storm the Marines operated Harriers in a V/STOL manner out of an abandoned airbase (capable of STOVL only operations) in northern Saudi Arabia (it's popularly known as operating out of a soccer stadium due to them setting up admin support in a soccer stadium next to the airfield). Despite the Harriers being marginally closer to the FEBA, a similar number of USAF A-10s were able to generate more sorties carrying more ordnance with fewer logistical bottlenecks by operating from a forward airbase capable of supporting conventional fixed wing operations. The Marines tried a similar thing during the invasion of Iraq, and have done similar things in Afghanistan (setting up a FARP outside Marjah a year or two ago, for example, to support Harrier operations out of Kandahar). The dirty little secret with all of these is that while they netted some impressive sounding metrics for the USMC and V/STOL, the cost that wasn't counted was the logistical effort necessary to keep these bases supplied with fuel, ammo, and maintenance support...as one example, one of the things that the Marines tout as being a benefit of V/STOL ops is reducing the burden on tanking support required by setting up FARPs closer to the action. That's all well and good, but you'll forgive me if I find it hard to believe that it is smarter/safer (forget cheaper) to truck fuel tankers overland outside the wire to a FARP on a road or parking lot somewhere instead of adding a few jets to the tanking support requirements for the day. The fact is that fixed wing aircraft (including USMC Hornets) were able to operate in the same areas more effectively and efficiently than Harriers doing V/STOL in each of the instances listed above, and this was due largely to the logistical burdens imposed by operating out of V/STOL only capable locations, which is why I think it is important to define what we mean when we talk about "austere" bases.
And all of the above ignores the very significant differences between the F-35 and Harrier: cost (if you think the raid earlier this year on VMA-211 was bad, imagine it with F-35s being the target...putting your hundred million dollar+ stealth fighter within range of any asshole with a mortar seems like a very poor cost-benefit tradeoff), LO maintenance, increased fuel requirements, the increased heat footprint of the F-35 compared to the Harrier...all of these things further count against it from operating out of an austere V/STOL only location. I should be clear, this isn't an attack on Marines operating fixed wing aircraft, or the MAGTF concept...I think both are vital components of the way the Marine Corps does business, but if we're going to assess an idea's value we need to be honest about all its limitations, and the idea of effectively operating F-35s out of a truly forward austere base where they can only operate V/STOL is a pipe dream.