There are obviously many, many good reasons a majority of people choose not use Priceline's NYOP method for airline tickets (no FF points, don't find out your itinerary until after purchase, inability to make changes, etc). However on a few occasions over the years I've used this product with 100% success and satisfaction.
First off, my travel is 95% leisure and I'm not tied (married!) to any specific airline FF program. Simply put, I'm not in it for the miles because I don't fly frequently enough to rack up enough miles to achieve worthwhile status. When I want to upgrade or fly on an award ticket, I transfer points from AMEX into an airline program and utilize FF perks that way.
Below are a few random experiences I've had with NYOP over the years.
1. SFO is my home airport. I'm a picky flier. If I can get to my domestic destination nonstop from SFO, then I'll do that any day over a connecting flight. My experience with NYOP has been that Priceline reveals the actual taxes/fees in their counteroffers. Having this information helps to determine if you're going to be assigned a nonstop or connecting flight. On the initial bid screen, Priceline calculates the maximum possible taxes/fees on top of your bid price. Again, it's the counteroffer that displays the actual taxes/fees you're going to be charged if you go through with the transaction.
On two occasions I've used NYOP from SFO to MCO because the taxes/fees in the counteroffer indicated a nonstop routing. And to sweeten the deal, at the time of these two trips, there was only one nonstop flight per day between the two airports (UAL), so not only did I know I'd be assigned a nonstop flight, but also the exact flight. If I were to do this again today, I wouldn't have the luxury of knowing which flight I'd be assigned because Virgin America now flies the route along with UAL. (I was pleased to see in the link that Virgin America is a partner with Priceline under NYOP).
2. Unlimited immediate rebid possibilities. Most people think they have only a few rebid possibilities (non-jet aircraft, selecting an alternative airport, red-eye, two connections, etc). This is not the case at all. Example: Rather than entering the airport city as your city of origin, instead enter a neighboring town, even if it doesn't have an airport.
Bid #1 - Enter Burlingame as your departure city, however on the next page select SFO as your choice of airport. If your bid is rejected....
Bid #2 - Enter San Mateo as your departure city, selecting SFO as your departure airport on the next page. If that bid is rejected.....
Bid #3 - Enter Berkeley as your departure city, selecting SFO as your departure airport.
So on and so forth.....
Priceline considers your enterting a different origin city/town with each bid as a change to a previously rejected bid. Priceline does not consider the airport you select to be your departure city for the sake of rebidding possibilities.
Using the above strategy in my previous bidding experiences has allowed me to increase my bid by $1 until finally reaching Priceline's target rate. For example, on one trip from SFO to MCO I began at $160. I made 11 different rebids, increasing by $1 each time before finally hitting the target rate of $171. With unlimited rebid possibilities, you can hit the target rate without overbidding by as much as $1.
3. On-line check-in. My last two NYOP flights, both times on UAL, I was offered the opportunity to pay to upgrade to Economy Plus and/or First Class during the on-line check-in process. So it would appear, with UAL, anyway, that they'll be happy to take additional $$$ on a NYOP ticket as they do from people traveling on any other "normal" fare.