Sounds to me, like it might be more cost-effective to just buy (and then resell), an old "beater" to get around in, for extended stays...
But then, the prices of those have also risen dramatically, of late.....
I think someone did this (and got some publicity for it) in the UK a few years back, when train tickets there got stupidly expensive. The biggest issue is dealing with registering it.
Depending on the timeframe involved, I half-expect to hear stories before too long of someone buying a beater under a fake name, driving it for a few days on the old plates and a bill of sale, and then just dumping it at a salvage yard (or leaving it at the airport on the way out) without ever registering the sale. To be clear, I am
not suggesting that anyone do this (not least because of possible liability issues, to say nothing of illegality), but I can
easily see someone doing that rather than fork over $1000+ for a rental or deal with all of the paperwork with buying the car.
Some posters on FlyerTalk have complained that rental agencies are not honoring reservations, but telling customers the price has gone up when the customer arrives to rent the car.
I sense this is going to end in a class-action suit or two (e.g. rich lawyers and
probably vouchers for the affected folks). This is a lousy position for folks to be in on the receiving end, but it reeks of fraud.
One suggestion has been to prepay for the rental, on the grounds that the rental company is probably far more likely to try and get you a car rather than do a refund.
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Bluntly, this is a part (albeit
only a part) of why I've been driving rather than taking the train (let alone flying). It occurs to me that an airline could probably grab some business if they were able to guarantee your rental car when you get there.