The intended purposes of tags are to allow people to highlight questions in areas of interest, hide (or at least deemphasise) questions in areas of non-interest, and provide some hints to the recommendation system (i.e. the "Related" sidebar).
However, people sometimes think that tags are the primary "on-topic" system: if it fits foo then it must be suited for the site.
I think that the questions you give as examples are interesting questions, and quite a nice way to add something to the "puzzle" side of PPCG: although they're code-golf, working out how to even begin answering is where half of the fun is. And certainly they do seem to group together in a way which fits the intended purposes of a tag.
But I would be very wary of the suggestions in comments and Nathan's answer for a tag with a broad name and scope. If we create a tag which people will claim as conclusive evidence that their over-broad under-specified question is on topic because "foo questions need an open spec" then I think the disadvantages will end up outweighing the advantages.
On the subject of the name, truly has it been said that naming things well is a hard problem. Your proposal of function-class seems to me too hard to pin down. functional-equation was my first thought, but is too specific. Maybe it will inspire someone towards the right name.
TL;DR: in principle a good idea provided that the scope is kept narrow, but the name needs some work.