Ultimately none of these details matter given the elephant in the room: you're voting on some app using your private key, and using some app to check with your private key if the vote has been correctly registered. But you have 0 way of knowing if the system is using this data in the way it was presented. For all the info you have access to, the system can just as well work like this:

1. You cast your vote using the private key

2. This gets registered on a server, it remembers "this person voted for X"

3. When you ask the system "who is my vote registered for?" the system tells you "X"

4. When computing the totals used to decide the election, the system returns 90% Y, 10% X, regardless of the actual votes cast.

Now, this very simplistic scheme would be easily defeated by asking them to publish the whole database of votes. But that would just break the anonymity guarantee of the election, so it is a no-go. And if they destroy the relationship between your vote and your private key, then again you can't confirm anything.

By the way, because you were citing Estonia's e-voting, I read up on it a little: they have all of these problems, and more. For now, people choose to trust the government, I assume and hope rightfully. But their e-voting system relies entirely on secure client devices, it relies entirely on trust that the servers are running the published source code, it relies on the proprietary closed-source client app being trustworthy. And people have even hacked their own vote to show that it's possible, which their supreme court found is not a problem with the election, since it was still their own vote. They barely even have some form of verifiability, and even that is relatively new.

I have no doubt that if a pro-Russia party had a realistic chance at winning (such that the populace and the incombent government would accept the results of an election where they won), Russian state actors would hack their systems and seek to get their people elected (whether they would succeed is of course hard to say). As would the USA if, say, a Latin American state used electronic voting and had an election where the decision was important enough. Or China in Africa, or Israel in the Middle East, etc.

> I think we both know that a corrupt government would not want to secure elections with merkle trees and publish them online. Too much chance of being caught, and they’d have no way to fudge the results reliably.

I think you seriously don't understand what a sham election is, what people know about it, and why it is done. Sham elections don't use semi-sophisticated means of voter fraud that could be thwarted by a better voting scheme. They don't have corrupt officials surreptitiously changing or adding a few votes.

They are entirely ceremonial affairs, where both the people voting and all of the officials know what the results will show beforehand. Often there aren't even options on the ballot. Even if there are, people choosing the wrong option will be threatened, possibly arrested for political crimes, etc. Everyone in countries with sham elections is well aware their vote doesn't matter, or it only matters in so far as the wrong vote can be like wearing an "I hate Big Brother" hat out on the streets in 1984.

The purpose of a mock election is to have some semblance of a normal electoral process to have a minimum of plausible deniability to facetiously claim you are following a democratic process. If people overall believed that the right way to do elections is electronically and by publishing a Merkle tree of the results, corrupt governments would hold sham electronic elections and publish made up Merkle trees.

You'll then have stories from journalists going and asking for people to compare their votes against the public tree, and seeing their votes are different. Just like today you have journalists coming back with stories of entire villages voting for the dear leader when local villagers say they didn't even enter the polling station. And it will matter just as little: the ritual of the election is the only thing that matters.