The term "AI" has been in use since 1956 to describe a wide variety of computer algorithms and capabilities. Neural nets and large language models fall very firmly under the term's umbrella.
What you're talking about is a specific kind of AI, artificial general intelligence (AGI). Very few people believe that an LLM on its own can become AGI and even fewer believes that current LLMs are AGI, so unfortunately you're jousting with a strawman here.
When you use the opportunity you have to cast a vote that could actually make a difference. Instead you're standing on the sidelines doing nothing except signal your virtue.
Then as I've said elsewhere, you're effectively not a part of the voting population and your preferences are not reflected in the results.
If it's in the form of shares so the cash value goes up and down over time with the share price. He's also prevented from immediately selling those shares, so it's in his interest to stick with Tesla and try to ensure that it does well. It's not so ridiculous an arrangement as most people are interpreting it based on just a few headlines.
One thing that I would consider quite nice about an AI politician is that you can run them through simulations and find out what they would do under various scenarios. Put the AI in a scenario where it's offered a bribe, put it in a scenario where it has to cast a vote on a particular bill, and so forth, and you'll find out exactly what sort of AI it really is.
Of course, consistency will depend on its operators. So there'd need to be some careful oversight.
Because Romney or McCain would have been so much better?
Those were your choices.
But when you die and an AI company contacts all your grieving friends and family to offer them access to an AI based on you (for a low, low fee!)
You can stop right there, you're just imagining a scenario that suits your prejudices. Of all the applications for AI that I can imagine that would be better served by a model that is entirely under my control this would be the top of the list.
With that out of the way the rest of your rhetorical questions are moot.
It's a question of whether you want to win somewhat or lose completely. Democracy is compromise; you're never going to find a candidate that perfectly aligns with your interests.
If you insist that you will only vote for a niche third-party candidate under a system like America's, then you've taken yourself out of the effective voting pool. Now neither of the two candidates who has a chance of winning needs to care about your interests at all.
It's similar to my own reaction to the people getting angry about Reddit data being used to train AIs. As someone who's been commenting rather prolifically on Reddit for 13 years I'm actually quite pleased by the thought that my views and interests are being incorporated into the foundations of modern AI. The only downside is that all those people I argued with over that period are also getting in there. :)