Ticket pricing is based on RM/IM algorithms which look at many factors. If the algorithm predicts that there will be heavy demand, it will only permit sales at higher fare buckets. If the contrary, it will open lower fare buckets.

There really is no such thing as a "walkup" fare and the concept is largely meaningless.

Historically, last minute purchasers have faced higher fares. That is because travel demand was so high that most flights were sold out or close to. That is no longer the case.

Thus, the answer is that it depends. Maybe last minute tickets will be cheap and maybe expensive. You will never be able to do as well as the algorithms, so it is not worth playing this game.