PCBs with components actually soldered to them become more delicate and uncomfortable to handle. I’ve seen projects with components being made out of the board itself (microwave passives, antennae, USB connectors), I’ve thought about using flextures from castellated edge-cuts to make a 3.5mm audio jack or battery holder, but that sort of thing would take a lot of trial and error and be less sturdy than a proper design. Stacking boards, or a board and a piece of acrylic, are definite possible methods for preventing hands from touching components, like how those convention badges (sadges?) are made.
But even if you could make an aesthetically routed PCB into a functionally electric piece of merch, is there anything interesting it could do? Anything with LEDs would look kinda bad without a diffuser, that could still be an option for a light-up coaster with a layer of frosted acrylic, though the frosted acrylic would cover the design of the board’s top. A mug heater with the PCB traces being the heating element?
It would be easier if the story had something as merchandisable as a nixie tube divergence meter. We’ve got the coaster, the conduit ring, maybe the spell rod or the feather wire tiara, and things like the student passes and Red Guard passes.