It looks like Southwest is also now showing prices on Google Flights (before, they might be listed but just a link to the SW site without a price). It always shocked me that SW would not allow their flights to show up on the biggest sites.
I do not fly a lot and I am not loyal to Southwest, but I welcome the change in direction for the company. My partner hates the idea of not sitting next to each other, so we haven't used Southwest on any flights we have taken together, as there is always that risk.
Hopefully, they can figure out how to turn things around AND also get prices in line. When I have checked their prices, I almost always find that other airlines have more competitive pricing (even accounting for the free bag).
Breeze is roasting Southwest in my neck of the woods. I just pulled up MHT to MCO R/T (during the next month or two) and best comparative prices are $138 (no bags) vs $362 (w/bags). Even adding bags, that is a pretty big delta!
Any ways, I don't use Kayak. I have used it in the past, but it doesn't seem as good at filtering as it used to be. Or maybe I just found better options.
I find Google Flights to be one of the better tools for checking flights and comparing options. But you need to know how to use it.