> On the other hand, if they were flying in a small airplane owned by one of them, it's illegal to split the costs of wear on the airplane, unless its a rental or air taxi.

This isn't true:

https://www.faa.gov/documentLibrary/media/Advisory_Circular/...

That AC and the regulations cited in it couldn't be clearer-- if you and the pilot are both going to $destination for $reasons, you and the pilot can definitely split the cost of the fuel.

Moreover, this is perfectly analogous to the carpooling example as you stated it-- two people both having a stated purpose traveling to a destination, both sharing the cost of gas/wear.

There of course could be ways to carpool where the passengers pay the total cost of the driver's gas/wear/etc. You can't do that in your airplane. But again, I think the reasons for this are glaringly obvious-- keep silicon valley from attempting to create an unregulated taxi service in the sky. (In fact, IIRC there was someone who tried over a decade ago-- perhaps these laws are a response to that?)

> Because of this, and other similar effects of FAA regulations, many small airplane owners own a company that owns the airplane, instead of owning it outright, and rent the airplane from themselves, whenever they use it.

I mean, the pilots I know who do that are either a) multiple people owning a single plane, or b) single owner literally running a rental taxi service. Who isn't covered by those two categories?