As wrong-headed as you claim my argument is, I strongly believe yours is more so. SELF-POLICING? Are you kidding me? The very first apartment I lived in in DC would probably have made it into some home and garden magazine for fabulous rentals, on the surface. The rent was NOT cheap, the paint, floors, windows, air conditioner, furnace, water heater, appliances, etc., were all new and well-designed. The house was fabulously landscaped. There was also a crack in the foundation that let water, insects, and rodents into the apartment, pipes that were probably illegal in the 1970's, and electrical wiring that hadn't been updated since Eisenhower took office. Fix what is cheap and obvious, leave what is expensive to fix and hard to find. Now, outside of hiring my own inspectors to check the electrical and plumbing systems and the structural integrity of the building, how was I supposed to see these things? The LL literally hid them by, for example, replacing outlets but not the underlying wiring so that it looked like he had updated the electrical and replacing the drywall near the foundation crack just before showing to hide the problem. Now, I was a kid then and didn't see the need to check their permits. Guess what happened when it finally got to the point where I was calling the city on code violations? No permits. Guess what that LL was trying to hide.
As for reputation, that might be all fine and dandy in a small city with a few landlords, but here in my urban world, landlords are almost as plentiful as renters. A majority of the rentals in my specific neighborhood (as well as many others in DC) are MIL suites in private homes (almost every home has one in my area). You may think that would help, as the owners have to live in the house, too. However, it doesn't stop them from installing cheap, old, used appliances (granted, easy to see in some cases), insufficient fixtures (hidden, of course), etc., and violating other codes like trying to rent out spaces that don't have 2 exits, even trying to rent spaces with no food preparation area (a minimum of a sink for food preparation is required...I can't tell you how many people try to rent spaces "no kitchen access," meaning there is no kitchen in the unit (just a bathroom sink, which does not meet code) and you can't use theirs, either). I went with a friend to look at an apartment, "all utilities included," yeah, because there were no heating or air conditioning vents in the converted basement storage room, so OF COURSE the LL didn't care if he had to "pay" for the utilities. These are the types of situations I think rental permits guard against. They are a bulwark against those who would rent whatever space they could find, legal or not, because they know they have to register it and, even if it's a maybe, be subject to inspections. If they don't register it, then, IMHO, they've got something to hide. It's not a panacea, but it's something, anything, to give a renter who's not willing to spend thousands on private inspectors (like a LL would rent to someone who insisted on inspections, anyway) some assurance that the apartment is up to code.
I suppose without permitting you could check to see how many complaints the property has in the code office. The reliability of this data depends on (a) how well the code office keeps records; (b) whether they record code violations by property or owner (lots of easy ways to have a new "owner"); (c) whether the LL actively tries to discourage or even intimidate tenants from calling the code office; on and on and on. I'm more than happy to pay a few dollars a month for my landlord to have a permit, as sort of a badge saying that she has told the city she is running a rental and isn't hiding anything.
Some places I have lived have tried to provide tenants with adequate information by creating online review systems for landlords and properties. As we all know, people are more likely to spend the time to complain than praise, and it's unclear whether there could be some fraud in some of these systems (for example, are these really the former tenants' reviews, or some office assistant instructed by the LL to go write glowing summaries?). Perhaps there is a better way than legal regulation...heck, I'm an economist, I like to see the free market work as well as anyone...but until the day I walk into an un-permitted apartment and it's immaculate and up to code, I'm going to doubt alternative, self controlling systems in this regard.