Boss gave no chance to go to the polls.
That's the issue that needs solving.
In a sane working environment, emergency absences should be allowable (personal health concerns, family problems cropping up, needing to stay in for the washing machine repairman) and even general flexibility for things that become fairly predictable for reasons out of one's control (every other Wednesday, the father can't pick up the kids from school so mum has to trade shifts to get across town. Yes, possibility of abuse (by
both sides of the equation, but can still be sympathetically dealt with in an unabusive employer/employee relationship.
Polling day is
known far in advance (in the US system, often
years in advance, barring extraordinary circumstances to either advance or delay such things). An employer who does not allow for (staggered, where needed) shift-alterations sufficient to allow participation in the democratic process is actually disenfranchising people. There should be no insurmountable problems here.
Even if the four-job single mother arranges with
all four employers to rearrange things for that day (prepared to do extra hours elsewhen; making sure there's cover by someone else happy to switch across; if the job needs such constancy) and then
just takes the day off, its maybe one day a year (or four) of 'sticking it to the Men', that is exactly balanced with the make-up shifts, anyway, so nobody should have problems with that.
Now, obviously, I know that employer/employee relationships don't always go that smooth - especially, but not exclusively, at the low-pay end of the market - but that is the root of the actual problem. Not the elections themselves. A sensible (and enforcable) employment law clause seems to me to be the answer to that, not "making polling into a weeks-long drag, hoping that everyone isn't on seven-day shifts at the wrong side of town".
Fitting 10k people through a single building would be fixed by both reducing the "early AM/late PM/
dinnertimelunchtime rush" by not so many people needing to zoom in prior to/after/during their working hours
and just properly provisioning sufficient polling-stations as suited to the balance of the community.
(I mean, so I don't have that perfect, where I am. If events turned out that I was needing to be two towns over for the majority of polling day I'm still registered only to pop into the pop-up polling station that's down on the main road to service my home neighbourhood of addresses. I actually went rolling on in there at something like 21:50 last time, probably the last "customer" of the day[1]. There's always occasional reasons not to have the foresight to rearrange commitments (or switch to some form of more remote voting), but this should be exceptional and not almost an inevibility...)
But don't expect me to wave my hand and fix the system (that isn't even my own), I'm just content to casually point out perceived problems that don't actually seem to be all that unsolvable.
[1] I made a joke of it "Hi, yes, I'm here now. Sorry to keep you waiting, you can go home now...", which seemed to be appreciated in the spirit to which it was intended, but have no idea if someone else had tried that at 21:45. Or someone else
even more tardy popped in at 21:50 (with or without the same quip).