If you don't want to pay application fees (which pay for those background/credit checks) and can find great places to rent that don't require them, more power to you! From what I've seen, they're pretty much standard, except in two cases: (1) newbie landlords who don't know to do those checks, or (2) landlords who specialize in renting to folks with terrible or no credit (like college students), so they don't bother. Though I suppose those who rent to college students often require a parent to cosign the lease... but that's a different conversation.
I like your used car analogy. The one who owns the car doesn't pay for the mechanic to check it out. The one who wants to buy it does. Likewise, the one who owns the rental unit doesn't pay for the background/credit checks/application fee. The one who wants to rent it does.
So to answer your question: No, I'm not worried. I may miss some quality tenants, but I'll also avoid some terrible ones. I'm OK with that. I only have 5-10 years of experience as a landlord, with 5 units currently... and I'm glad I do the checks.
Not sure I agree with your "owners" model. Contrast that with banks and mortgages. Despite the house owner "owning" the house, they still have to foot mortgage insurance, despite the bank being the beneficiary. In this case I feel if the bank is doubting the people's ability to repay the debt, they should bear the burden of the cost. I've had companies request driving abstracts or even want to drive with me for a bit before driving company vehicles. Again the company, despite owning the vehicles covered these costs.
You are correct in that when I lived in Texas I noticed application fees were more the rule than the exception, In Canada very few places have an "application fee", and it's a minority ask for a credit/background check. When I lived in Indonesia on the the other hand, the going rule was two years leases and the lump sum rent upfront.
The bottom line is that the best tenants, borrowers, employees, whatever get the best terms, and generally the reliability these people offer more than offset those better terms for whomever's on the other end. Companies or people with AAA credit ratings aren't going to the payday loan shop on the corner and paying 75% interest.
At the end of the day, I suppose it is simply what the market will bear. So things like background checks or having to come up with $75k upfront or committing to a 5 year lease are really just additional costs/hassles to the renter, so to say I'd simply move on is an exaggeration, but the rent would have to be below market enough to more than make up for it.