Rate-related effects might be show stoppers. What happens at a high rate of charging or discharging?
Heating? Swelling of the membrane? Hydrogen and/or oxygen evolution?
Any of the above could lead to physical disruption of the device and/or explosions...
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Question: What happens to a fully charged device when you "crowbar" it (dead-short it with a conductor capable of handling the current)?
And the potential to turn into a plasma grenade.