Show up to the interview clothed, be pleasant and polite, show off your game, and leave it at that.
As an interviewer myself, I get where they're coming from. My email is not shared with applicants, so finding it requires some stalking or at least digging me up on LinkedIn. By the time they reach out, I've already put in my notes, and any final decision is out of my hands. So while I'm not going to hold it against them, it's not a particularly useful move on the candidate's part either.
Should work in a job interview setting as well.
It also has the benefit of giving me a signal. Usually if the interview went well, the interviewer will happily agree to be connected. If not, you'll see either a refusal or subtle body language indicating discomfort with the connection. And you can then form your own conclusions about the probability of getting an offer before the firm gets back to you (or often ghosts you.)
Use every signal your prospect gives you.
How can you determine if a thank you note is genuine or not if you don't read it in good faith?
One person might send a generic thank you that tells you nothing, and another might send a thoughtful message that in some specific way reiterates their interest and excitement in the job.
> ...and has no impact on anything...
Sure it does. I hired lots of people in my career and things like this helped me determine if the candidate was thoughtful, professional and interested. On multiple occasions, I hired people who didn't technically meet my ideal requirements but explained why they were interested in the role and gave me greater confidence that they were up for the challenge and worth taking a chance on.
Cynicism by default does not serve you well in any aspect of life.
You sound like someone who most would absolutely dread to work with.