I asked Jan to enter the discussion as she is a provider to these sites. So see her response to you below. I will add:
Your statement: "It should be pointed out that Realtor.com, which is by far the most popular site, is a direct feed type of site, but typically only if your agent's broker allows that..."
Before the policy change, the only way a listing did not show in Realtor.com was if the broker checked "no". So your statement about the borker "allows that" is no longer the case. NWMLS does not do it even if the Broker "allows it". The broker must employ a separate service, like Jan's. Consequently, the method of an offices listings being on Trulia or Zillow or Realtor.com are pretty much the same, without any automatic or preferential treament via NWMLS for any of them, or similar sites.
The BIGGER issue is that the manner that this feed is implemented is via a NWMLS download agreement, and each office or broker is drastically limited in the number NWMLS will provide. It used to be two, but when NWMLS stopped the feed to Realtor.com, Jan and others managed to get an additional ONE approved, making it three. Still not enough to feed to multiple sources, since the broker uses one for his one site. This is why agents are not free to have their own site with just anyone, as agents don't get to have a "download" agreement and all agents are subject to the limited feed access of the broker.
Big issue...It would seem to me that a broker doesn't have enough feeds to do all of them...so they have to choose one vs. another at present, given they only have 3 feeds and two are usually already being used by the broker for other office purposes.
Originally Trulia was a "scraper" site and pulled listings from anywhere on the web without approval by the owner, the mls or the agent. At that time you couldn't individually list a home on Trulia. They changed that aspect, but I don't know if they eliminated "scraping", and am pretty sure they have not. So a listing may show because the listing appears on an agent's site and Trulia "scraped it", even though no one approved it to be there.
You may remember that Trulia elected to OPEN in NYC (as I recall) an area that has no MLS, making a scraper site quite invaluable to potential buyers.
Your assertion that Realtor.com is the "most popular" may or may not be true in any given area from time to time. In some areas it is Zillow...in others it is Trulia in others it is a local brokerage site, as to the potential buyers of homes in that location.