This seems to be an obvious idea, but a cursory search didn't catch it described. So, a suggestion was raised in a nearby thread about a specific case of tools' quality mattering. A few arguments later, I thought about it some more, and I can formulate it better now.
Most tools in the game are used to harvest resources in one way or another: axes to cut down trees, saws to cut up logs into boards, and so on. All of these tools have a quality level, yet it only seems to affect things on the saw, and the way it does doesn't make a whole lot of sense. I suggest that tools' quality be (ahem) re-tooled to work somewhat like with the Symbel items: instead of representing something unique to the tool, it primarily represents a general state of "durability". Every time a tool is used, its quality/durability has a chance of being lowered by one point. When it hits zero, the tool is broken, cannot be used any more and must be replaced.
Secondary: It is possible that the quality of tools that are required for a job (Only the saw comes to mind, but I'm not that experienced with the game yet and I may be missing something) affect the job's success rate (Or, if a single use of the tool provides several pieces of a resource, the amount you get). This should cap out at some quality level at or just below 100%: at this point, the only difference between a quality n tool and a quality n+1 one is how long it'll last you.
Reasoning for the primary part: if an item has a quality level, it should somehow matter. Tools that see near-constant use tend to degrade with use. It makes sense for their quality to work this way. Furthermore, if a resource is there, it's there: you either can get it, or you can't. Having a better shovel will not magically make the clay or soil you dig up make it better than clay or soil you dug with a slightly sharpened stick.
You may argue that you may get at some things too hard to be too hard for a worse tool. Unfortunately, the way quality nodes work right now, you can't simulate it, and I think it'd be too hard to pull off. It does bring me to my reasoning for the secondary part: take, for example, a saw and cut a log into pieces. You won't make the wood itself worse by using a blunt saw: you'll just take longer and possibly not cut as straight as with a good one, in effect making fewer boards - but they will be (almost) exactly the same boards.
Note that this should in no way affect the more advanced constructible tools that convert lower-level resources into higher-level ones or end products, for example, looms or kilns.