the ReferenceTooltips gadget loads on all pages, but can only be used in devices where a mouse is available (and thus it is possible to hover over references).

Not correct: tooltips are just activated by click on touch devices, not by mouse hover. In fact, ReferenceTooltips even allows to read tooltips over <abbr> tags (for example, here in the "Historical population" table) that are otherwise unreachable on touch devices.

We could also just allow skip functions to be defined the same way as other JS code, on a JS wiki page (maybe with some built-in defaults).

Yeah, I think, if the future is ‘drop the checks entirely and load the same bandwidth of gadgets at mobile and desktop’, checks in the gadgets themselves seem like a much more sensible path than whatever skip functions are. It’s not like this kind of system would simplify anything, unless it was something more generic like a gadget with a skip page defined implements a module that only returns a check for its requirements, and only when the check is true, loads its JS to users. Doesn’t seem much sense to implement this for two simplifying writing a few JS variables.

If anything, it is kind of problematic in the same sense that JSON pages addition was: testing gadgets as interface admins would become harder because there might be a possibility that their code doesn’t work in its entirety and the reason isn’t noted anywhere in the code itself (with JSON pages bundling, it became harder because of require, gadget authors have to add debug variables for their testing now).