Imagine being a recruiter, seeing someone genuinely interested in the position (or at least willing to put in the effort to make it seem that way), and getting annoyed rather than hyped. You in the wrong line of work, brother.
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.