My guess is it comes down to a desire to keep this work from happening at the gate. Southwest is pretty conservative so it makes sense to me that they physically want to see your passport at the airport. The fines are also pretty crazy if they send someone to another country and that person isn't admissible. So if they didn't check it at the ticket counter, they would check it at the gate which could interfere with boarding times and quick turns.

It may also have something to do with a lack of prioritization. If they are anything like the companies I work with, they probably have long backlogs of IT projects waiting for resources or budget to be accomplished. If international flying is a relatively small part of Southwest's business, it makes sense this enhancement might not be at the top of the list compared to other projects which would benefit more customers, involve less risk, or are less expensive to implement.

It would be interesting to see what Southwest has to say if this is something they can comment on publically.