Or, you could just - make some knives.
I started with 5 skill in toolmaking, and can now make every tool I have heard of - except shovels, for some reason.
Being that Im a crappy tool crafter, I could but then I would have crappy tools for my good weapons, or good wood, or good armor etc.
If I were just skilling up ya you would be right, but Im crafting good stuff, QL of the tools matter, just as in fighting QL of the weapons matter, just as in cutting down a tree, QL of the axe matters.
If you are making tools for grinding be sure to use foragers or scrappers tools to make them. Using those two sets gives the product a higher durability, meaning you can spam more before they break.
If you are making tools in order to have a good set to make "real" items with be sure to use pioneer's or trapper's tools to make them. You get a bonus to QL of the product when using them.