It’s certainly an improvement, at least for the root/boot partition. Though it’s misleading, as the warning fires well before the partition in question is truly full, it at least gives a much better indication of the problem than “boot partition failed.”
Most of the time, you don’t have a specific log where to check the problem (see for example the disk usage case).
Often you need check multiple things inside the system.
I think a better solution is a link to a documentation for the specific problem which a detailed description and list of resources on how to solve it.