Building a rechargeable device that allows for fully offline Bitcoin txs to happen would make it about invincible even in disastrous events. Is this a bad/impossible-to-realise idea? What do you think?
Sorry, I think that the solution is missing something important and it becomes kind of worthless as it is.
Imho
complete blackout of the entire internet and electricity is not really possible for reasons like shortages. Or, let's say, the chances for that are way too small to matter.
Imho the only actual problem is massive solar flares/coronal mass ejections/geomagnetic storms which can indeed shut down... maybe everything. But in such a case even the satellites aren't safe.
I don't know what would be the correct solution, but we seem to try to address problem with lower chance to occur and it may be better to focus on the bigger problem; if that's handled, the smaller one will also be solved.