Not sure, but I feel the toolbelt isn't currently entirely working as intended.
While using it for chopping wood blocks or trees down, an axe is summoned from the toolbelt, as intended.
However, when I begin to destroy things, it doesn't make use of the axe to aid in destroying.
Given that you are supposedly able to use a scythe from a toolbelt when harvesting, shouldn't it be possible to use tools in whatever they can aid in, not only for where they are supposed to be used?