There are many reasons.
- Price is the number one reason. WN is almost always cheaper for walkup fares, sometime by very significant sums of money. This is particularly true if you are flexible as to the destination and/or origin airport (i.e. flying SEA-FLLThat alone is a huge reason to fly WN. WN will occasionally beat AS' lowest fare on advance purchase fares, but this is infrequent.
- High frequencies in some major business markets. Nobody beats WN in the Bay Area to SoCal market as far as frequencies and choices of airports go. WN flies OAK/SJC-LAX/BUR/ONT/SNA/SAN on full sized jets multiple times a day to each destination. AS flies one flight a day between SFO and LAX and four flights a day between OAK and SNA. UA comes close with lots of flights between SFO and LAX but you'd better be prepared for CRJ's and props if you want to go to BUR or ONT.
- Ability to bank unused tickets for a year against multiple itineraries. AS charges $50 to move funds spent from one ticket to another and even then you can only use the funds toward one ticket.
- Some people actually like the fact the WN employees are corny. I prefer AS' more professional approach, but to each their own. WN's service is certainly better than the bitter stuff so common at NW and AA.
- You already mentioned Rapid Rewards, but there is something to be said for completely unrestricted award inventory.
- Did I mention no RJ's?
That said, if given the choice between AS/QX and WN, I'd pick AS/QX in a heartbeat if price were close.