Suggestion for the UI: While the progress bar for mining is active, highlight the axe tool slot. If there is an axe, make it green. If there isn't one, make it red and flashing. This will emphasize the true importance of the axe, and call attention to the problem and its solution when players might simply suffer without knowing why.
This can be a purely visual change, and have no impact on active weapon selection, so players would continue to be able to do this if they wanted.

(This would tie in well with my other suggestion recently about the axe as a first-class SMG-like weapon/tool for reviving ghosts, but it can function on its own so I made a separate post. Regardless of implementation, as a purely visual guide, this would be a simple change to help new or returning players understand what is going on.)