Is there such thing as a button-cell light with a die-style emitter? Or are they relegated to the 5mm plastic LEDs? I would imagine that power, heat, runtime, packaging are issues.
Problem would be current draw. Those button cells are intended to produce a few (<5) microamps for a long time - not multiple amps for 0.00004 of a second.
I’ve never seen one for sale, but it’s not a crazy idea. Power LEDs typically have better lumens/watt efficiency, so even though it would need to be rather dim because of small battery capacity, you’d still end up with a light that’s either a bit brighter or runs a bit longer than a 5mm.
Only disadvantage is, a power LED gives you a wide flood beam unless you use a reflector or lens, and that would make your light a lot longer.