No, it only gives a false sense of security, which is worse. Everything you are describing relies on trust in the people that build these systems, trust in the people that invent the algorithms, trust in the people that invent the maths, trust in the chosen parameters of the cryptographic systems, and so on. Literally none of what you are describing works if you don't trust in all of these people to be (a) honest, and (b) really really good at what they're doing.

Now it's getting a bit silly. Imagine saying about all the technology infrastructure we use daily, such as electricity and computers, that since they require "trust in the people who built these systems, trust in the people who invent the algorithms, maths, and parameters of the curves etc" therefore they are giving a "false sense of security". No! The math isn't just arbitrary, the people aren't just cobbling together a computer I happen to buy. There are literally standards bodies, scientific literature, audits and much more. There are entire ecosystems for error-correction. Otherwise, throw away your technology, you're trusting phone and computer vendors, you're trusting mathematicians with math, and scientists with science... and that's actually worse than living in a world where you fetch water yourself from the river. What? No, it's not.

If you're down to those kind of arguments, I and people like me would conclude that you're out of good ones, and we have a good solution after all.

A paper ballot system isn't great at all -- it is far too slow and expensive and frustrating to run an election, and voter turnout is low for traveling and standing in line -- and certainly it is not "proven secure enough in many thousands of elections". Many elections around the world are disputed, contested, insecure, and the ones you think are secure, are also contested (e.g. the 2020 election, the 2000 election, the 2016 election). You dismiss it in cases you like (US elections) and are happy for your politicians dispute it in cases you don't like (Venezuela) etc. Even if the Supreme Court of Venezuela weighs in, you wouldn't trust it. It's a canvas on which everyone can paint their own outcome, and claim the other side "stole" the election (as if their side didn't engage in similar shenanigans to cancel it out).

If we switched to electronic systems, verification would be so cheap that anyone could do it (as it is for, say, verifying files you downloaded from the Internet with a checksum, which wasn't always the case with previous technology such as analog-to-digital MoDeMs without cryptographic security) -- not only that but it would enable so many more applications. Imagine using Git version control without a SHA1 checksum, and just "trusting the system" to never flip a bit. Imagine not being able to use Merkle Trees for downloading files, verifying their integrity, etc. These things not only improve security and reliability at almost no cost, but enable a whole class of things that would be impossible with pen and paper. Seriously you don't see a difference between, say, BitTorrenting movies and Roman scribes copying into a clay pad? Oh, but we're trusting people who discovered electricity, invented general-purpose computers and the hash algorithms, what if they're trying to trick us and will finally rugpull us all in 2025? Alan Turing and John Von Neumann will have the last laugh as we'll all download the RickRoll files instead of the ones we want.

Nothing you are describing can prove anything. It all still relies on your claim that you were trying to vote X, but the system registered you as voting Y. It's your word against the system. You can be convinced yourself, but you can't 100% convince anyone else.

Not at all. If someone was able to record a signature that their voting gateway signed vote for X as vote for X, but then later that same service claimed they voted for Y, they are caught red-handed cryptographically signing with the private key two conflicting votes. You're equating that to some villagers telling some journalist on camera that they never voted. Ugh. One can be verified by anyone, the other is just hearsay by some journalist.