Thank you very much for the feedback!
I wanted a strict 4-way movement scheme and no analog control (such as a mouse) specifically to make it play and feel more evocative of arcade games like Dig-Dug or (while not technically an arcade game in origin) Bomberman, but one can chalk that up as a matter of taste and mine is perhaps outdated which is still something I should keep an open mind about as a developer.
The intention with the ax is to charge it up for stronger hits rather than spamming it, and one can move while charging their swing, but it was a behavior I noticed in Vimlark's stream of the game. Some in game direction to direct the player to try holding down the button does seem to be in-order