The reason you don't see people renting expensive assets to each other on Craigslist is because the nonmonetary transaction costs are too high. When someone wants to rent a car, they're looking to straightforwardly solve their problem in a predictable manner. They don't want to sift through different Craigslist ads looking for one that meets their requirements, emailing to see if it's available, figuring out if the rental is legitimate, etc.
On the lessor's side, since the primary market prefers bona fide businesses you're left with the customers who cannot rent from the primary market. Meaning you're much more likely to end up on the receiving end of abuse (outright theft, vandalism, being an accessory to a crime), or at the very least problematic customers ("I know I rented it for one day but I have to pick up my kids tomorrow so I'll return it Thursday"). A business can absorb such variance, or at least create the illusion of doing so, whereas for an individual such events present a major hassle.
You can bundle all of that transactional risk up into a kind of insurance, but that only works if you're large enough that the insurance company can verify that you're not defrauding them.
