We have a secure, provable, relatively cheap method right now: Paper ballots and public observers at elections. Compared to the stakes the cost is peanuts.
The fact that virtually anyone both capable and eligible to vote is also capable of understanding the voting process, as well as what kinds of physical acts are signs of fraud means that many more people can evaluate the process, and determine - even just by looking - whether something fishy is going on at their voting station.
Your average voter will be easily convinced that he "doesn't know enough to judge" whether something is fishy with his voting machine, even if something seems to be clearly malfunctioning; "oh don't worry sir, the print out might be wrong, but your vote was definitely counted correctly internally".
The rise of any form of electronic voting is really troubling - and don't even get started on anonymity concerns...
It's basically a login that's tied to a piece of paper containing a hash table of numbers you use for two factoring.
It's the safest citizen verification system we've ever had and it's basically used for any for of identification in the digital world from banking to using our public sector.
Our government as an example used it to send digital mail to everyone in a secure mailbox called "eBoks" saving us billions in not sending paper (and bankrupting our postal service as a side effect).
We still use paper ballots for elections but it's frankly easier to fake an identity using those than if you were to sign in with "nemId". Today all you need to be allowed to vote is the paper you received and the right sex/age range. So basically I could vote for my brother if I obtained his ballot. With NemId I'd need his username/password as well as his keycard.
Obviously you'd have to anonymize it, but some digital systems being broken doesn't mean they all are or that our current system is that great.
I've observed elections in the balkans, and they sure aren't safe or democratic despite being done they way you prefer, because it's so easy to exploit if you manipulate the paper trail.
1. I take someone's ID, I look them up on the voter list. If they are not on the voter list I take their proof or the sworn testimony of someone that does live in the district that they live where they say they live. Either way, observers can record their name and supposed address.
2. I hand them a folded ballot and they go, with assistance from a family member if necessary, to behind a security wall to mark their ballot.
3. They place the ballot in the slit of the box, folded so their vote is secret, but visible to all observers so that they couldn't not have snuck in a second ballot.
4. The ballot box never leaves public view. In the event of an emergency I take the ballot box and hold it high so that everyone can see it, especially the observers, until we get outside.
5. Anyone in line by the time the polls close is allowed to vote and number of voting locations are determined by a public service (not politicians) so we don't disenfranchise voters or unduly burden voters.
6. In full view of my assistant poll clerk and all observers we count every ballot. As DRO I have final say over questionable ballots. If I make an obviously unfair call observers can alert my superiors at Elections Canada. I only had to make one decision on one ballot out of around 500.
7. We compare the count of people, the count of the ballots we gave out, and the count of the ballots in the box. These all must match. If they do not match we count again. It's harder than you'd think because people accidentally fuck up ballots or someone can have the same name but be a different person. This can even happen at the same address! Usually a son being named after a father.
8. I fill out the vote totals and give one copy to Elections Canada, one copy to each party observer, and I keep one copy for myself. We then put security tape around a tamper evident bag with the original ballots for them to be counted again by Elections Canada HQ.
Now tell me, how are you going to fraud that system? We wrote down everyone's name, at most you might be able to get someone to vote on behalf of their brother here or there. Or the people voting by mail might have their ballots disregarded or changed, but most people vote on election day and Elections Canada is trustworthy and explainable to anyone.
I could never fully trust your NemId system because you could never prove to me that everyone that supposedly voted existed. In Canada's system we can literally count the people walking through the door and we can literally count the individual ballots.
Aside from that it's literally impossible to obtain a nemid if you don't exist, and, once you cease existing so does your id.