In order to do an analysis you have to start with facts, not speculation. Speculation will only skew the results.
We need to know the following:
For the purposes of discussion, I believe most of these "facts not in evidence" can be reasonably guessed.
Aircraft make and model? I realize it was a B-737 but which variant? How was the aircraft equipped?
Irrelevant. How many airliners are not equipped for a visual approach? How many airliners used commonly in passenger carrying operations do not have some kind of instrumentation backup for approaches of some kind?
Any MEL/CDL items in effect at the time of the flight?
While not necessarily irrelevant, certainly those items cannot prevent a visual approach, or they would not be on the MEL. Might make it more difficult, but not impossible.
SWA procedures for approach at night (visual)?
While this is an important question, you, yourself, have noted the SOP at most of the airlines are backup with approach guidance on visual. One can "reasonably" conclude that, since it is in the name of safety, those procedures are pretty much standard in the industry.
Duties of PF/PNF during approach (SWA procedures)?
Again, an important question, but once again, you can pretty much bank on the SOP being the same or nearly so as you have in your procedures.
Briefing. Was there an approach briefing detailing the arrival and approach? Where fixes identified, verified on the chart as well as the FMS?Was the NAV accuracy verified on the FMS? What is the maximum drift allowed? Where the Navaids hard tuned or where they auto tuned? Was the airport diagram referenced in the briefing pertaining to approach lighting, landing aids and exiting the runway? How were the respective ND's and PFD's configured for the approach?
If not, then we have pilot error.
ATC. What altitude does radar coverage go down to? Does the tower at Branson have a scope? Did any controllers notice the aircraft was off course? Was the crew asked to verify position?
Although certainly a help, it is not ATC"s resposibilty to fly and land the aircraft.
Human Factors? How long had the crew been on duty? Was this their first?second?third?forth? sector of the day and what day was the trip sequence in (first, second, third, forth?) How much sleep did the crew have in the previous 24 hours? 36 hours? 48 hours? Was there a change in their schedules? Recency of flight (day or night) into this airport for either crewmember?
Certainly agree on these, but it does not absolve the pilot of making the errors.
What do the Captain and FO's training records look like? Any problem areas?
These, again, are pilot problems. Yes, if there were problems in their training, it should have been dealt with, but does not absolve them of responsibility. (for purposes of discussion, not punishment.)
Any other carriers or SWA had previous problems with this airport in the past? Ongoing issues?
Even if so, There were plenty of ways to insure success in the flight that were not availed upon.
This is just a small sampling of questions just to begin the process. I don't think anyone here (unless someone from the FAA or NTSB working the investigation) has these answers yet.