A key feature of a secret ballot is that it must remove the ability for anyone to verify how you voted even with your cooperation (no matter if willing, coerced or bought) - you must have plausible deniability i.e. any reasonable "demonstration" to others how you voted must be possible even if you actually voted differently.
And for context on the scale of this, in the 2020 election there were 65,642,049 mail-in-votes cast. And the outcome of the presidential election was decided by 42,921 votes. [1]
This keeps coming up but is not generally true. See my comment from another thread [0]:
I don't know how it's done in the USA, but in Germany voting by post has to be carried out before the day of the election. The actual postal votes are stored and only opened on the day of the election. After somebody send in their postal vote they can go to the public voting office and declare to invalidate their postal vote. The people counting the postal votes will get a list with invalidated votes and remove these envelopes before the votes are opened. The person who invalidated can then either do another postal vote or vote at the ballot box.
So in Germany postal voting is secured against selling votes.
Which is why mail in voting is a bad idea
Just because bad things are happening doesn't mean people need to like more bad things being made easier to achieve
What does "verified" even mean here? At the end of the day, you need to convert it to some cryptographic key, and then that key is vulnerable to attack: either it's kept in the voting machine, in which case the machines themselves are a single point of failure, or else it's given to voters, in which case their insecure phones, computers, etc are easily compromised to get the keys.
Checking your votes doesn't help: a significant number of people do not vote. An attacker can submit votes on behalf of those people using their keys and noone will know, and even if you find someone who claimed that they didn't vote, how would you ever prove it either way?
The advantage of a physical system is that there is no single point of failure: changing the overall election result requires a physical presence at multiple polling locations. All electronic voting solutions are intrinsically worse in that respect.
That's a problem that hasn't been solved at all by the current applications of cryptography.
Even if my computer gets hacked, as long as I can trivially search my "confirmation id" from another device to ensure it's what I cast, I'm going to see if it was or wasn't tampered with.
Having public records of votes on a per vote basis with multiple layers of cryptographic signatures at each stage of processing them would be a world of improvement over the current system, both client side and server side attacks considered.