We are in the midwest, and that has been my experience as well. Flights on SW from our airport are never cheapest right away.
The good thing about Southwest, even in non-Covid times, is that if you see that the price goes down, you can get a credit for the difference. Now, if you do not fly a lot that may not be a huge bonus to you, because that credit does expire after a year (although I think you can get it extended, maybe?). But if you are someone who is pretty sure they would/could fly with Southwest again in a year, then there is no harm in booking right away and then watching for fares to go down and grabbing a credit for the price difference.