You have a good point here.
Right now there are only two different axes: the rudimentary and the bronze one. Bronze one is way more efficient (harvesting time is reduced). There will be other metal axes but they will not be more efficient, only last longer.
The question is, if we remove tool assignment, which tool will the game automatically choose? Maybe you'll want to keep the good axe for oak trees (which are long to cut down) and use the worst one for fir trees.
Also, suppose you have a bronze axe with 1 use remaining and a rudimentary axe. Suppose the game choose to use the bronze axe first. You select a fir tree and it shows 2 hours of work required. Then you select another fir tree and now it's 4 hours required. Maybe it's ok, but so we need to display some information.