Are you suggesting a way to verify your vote was counted correctly is needed? Wouldn't that provide the ability for folks to sell their vote by being able to show someone else?
An example: https://en.wikipedia.org/wiki/Scantegrity
That's why some states don't allow you to take a picture of a ballot that you filled out. They're trying to prevent you from confirming that you voted a certain way.
Or have a person follow you and see what you do. Which would've worked all times I've voted here in Sweden.
Secondly, there are states where you can vote by mail. Do you know if vote selling is a big problem in those states?
It's not about you selling your vote, it's about coercion. If your vote is verifiable, then you can be threatened with bodily harm for not voting a certain way, and/or for failing to verify that you voted a certain way.
Your freedom to sell your vote is worth less than someone's freedom to vote free of intimidation or threat of violence.
The state republican party still makes occasional claims of voter fraud, but those are exceedingly rare -- something like 54 ballots out of 4 million in the 2016 election cycle -- and they mostly come down to people voting in Oregon and in another state at the same time.
The only reported case of election fraud I can remember was in 2016 and done by a republican, in which she tossed out a bunch of democratic voter ballots. That's it.
For two decades of elections, Oregon hasn't had a problem with election integrity. They do, however, have a consistently high turnout, which they attribute to vote-by-mail.
And this is a real issue, vote buying and cohersion has historically been the most common voter fraud mechanism in the US. It's a major part of how the Boss Tweed and his associates ran New York.
This is less ideal than voting in person for everyone, as it still has failure cases like sufficiently abusive relationships. But it's an overall improvement over the previous system. Significantly more of the population votes in practice, making the vote a better measure of the ever-nebulous "will of the people".
The fact that you cannot personally verify whether your vote gets counted is a feature, not a bug.
I'm certainly not going to pay you to vote the way I want without proof of delivery.