I would imagine the glass being either too heavy for the switch to hold open or too brittle for regular use (especially the cross post).
not necessarily!
See you can easily make glass or ceramic keycaps that are tougher than PBT. Also, you'd have to design around the stem a little, but it's possible to harden the stem up a lot. I was thinking of sintering some ceramic powder keycaps, but getting the size right would be hard. I suspect you'd have to machine the cruciform stem a little.
Long story short, it'd be a lot easier to make hall effect keycaps in basically any material.
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About injuring yourself after hitting a keycap hard: I don't think so. See, you could make it so that the cap bottoms out on the switch housing which would seriously dampen the force. I doubt it'd break at all, but a nice glass-ceramic composite keycap would be more than tough enough to not shatter. Also, such a material would break into large sections rather than shattering completely. Also, you could design a stress raiser so that just the top would shear off safely. There's a lot of ways of making it safe.
TBH I think the hardest part would be to ensure that there's enough friction on the stem to keep the keycap in place.