No matter if the vehicle is safe to fly or not, some people may not feel comfortable flying on one. The only justification of overturning 80+ years of airliner industry precedent in eliminating the specific vehicle type from the descriptions is to deceive.
Here's the a/c type on southwest.com desktop, right now: https://imgur.com/a/B6PxsbB
I don't see it on mobile, but I don't think it's ever been there.
https://www.linkedin.com/pulse/how-identify-boeing-737-max-l...
[1] https://commons.wikimedia.org/wiki/File:CFM_56_Lauda_737.jpg [2] https://commons.wikimedia.org/wiki/File:Classic_Colors_South...
But you're still at the mercy of the airline. If they do an equipment swap, you're not entitled to change or cancel. You'd only have the option not to fly, forfeiting the cost of your ticket.
As someone else in this thread said, just fly Delta (domestically).
[1] https://www.aa.com/i18n/travel-info/737-MAX-return-to-servic...
[2] https://www.united.com/ual/en/us/fly/travel/inflight/aircraf... (under "What if I don't want to fly on a MAX?")
[3] https://www.southwest.com/737-max/#return-to-service-plan (under "What are Customers' options if they don't want to fly on a 737 MAX?")
Better just to avoid Southwest.