Voting, much like all other things in Estonia such as getting married/divorced, doing taxes, signing documents, starting/closing companies, notary dealings, bank dealings, selling/buying vehicles, and many more things I can't even think of right now are entirely done via the digital ID that every citizen has. This means that you authorize/sign actions with it, including voting, because only you have your private keys (either in your personal ID card, in your phone's sim card, etc) that you yourself know the PIN for, which then authenticates you as being you. I think we're now at a point where there isn't a single government or business dealing you can not do entirely online (https://e-estonia.com/solutions/).
> in your phone's sim card,
Phones and sim cards a lot more temporary than ID cards. I don't know of a lot of theves that target ID cards for their authorization uses. Phones... people will steal those.
You can close your Mobile-ID when your phone gets stolen so the security keys on it will be useless, and even if you don't close it, nobody can use your security keys without your PIN, which is in your head.