Very large apartment complexes (e.g. Stuyvesant Town) tend to have in house sales staff. Although even there some poor schlimazels end up needlessly paying a fee.
If they directly charged the landlords, maybe some of them would consider whether the service is worth 10-15% of a year's income.
Also, for all the reasons mentioned in potatolicious's other post [1], it's difficult for a landlord that is renting directly (i.e. without a fee) to convincingly communicate that fact to potential renters.
I wasn't renting in the Dinkins' era, but from what I hear it was an entirely different story.
I went through a broker and a super fast, easy, and great experience, but I was also wary of dodging some of those spammier looking firms you see on Craigslist and other places. Good luck finding no-fee places on Craigslist, don't even try. No-fee seems to be viable only if you scour the city for buildings that display their management info and you swoop in at the right time to claim a place directly. Alternatively, take over someone else's lease.
I've seen coverage about some NYC apartment startups recently, and while some of these features are useful, I keep hoping for someone to come in and actually fix the core problems with NYC real estate - i.e., brokers.
There was a startup that had some buzz locally a few months ago when they launched who claimed to be upsetting the broker order, except it turns out they were doing this by becoming a mega-broker themselves and charging basically the same brokerage rates as brokers. Meet the new boss, etc.
If there's any aspect of NYC that desperately needs generous application of our "disruption" buzzword, it's renting.