Intuition is a valid theory. Let's say you see a tree. You don't see a bunch of shapes and light and then deduce that you're seeing a tree, but it just presents itself as a tree fully formed. Likewise, if you were blindfolded you could still perceive the tree and have an accurate mental image of it through touch, sound, smell, or other senses which you're likely to engage looking at a tree anyways. There's no single sense that accounts for perception and even in people who don't have synesthesia sometimes you have phenomena like flashing a light and playing a beep twice and people seeing the light flash twice. Therefore, people have perception that's not strictly sense-perception, though calling it "ESP" at this point is as problematic as calling something in the sky that you can't identify a "UFO" even if it's technically correct. Just because something's a valid theory doesn't mean it can justify anything you want though and that causes problems when people try.

Also, I think typings should be done scientifically which means not only using intuition even if you're good at it and love it because I don't think any intuitionist worth their salt only uses intuition any more than any empiricist worth their salt only uses their senses or any rationalist worth their salt only uses reason. I think socionics itself would encourage that since it doesn't have IMs that exist outside of the context of being paired with another IM unlike MBTI which just bizarrely measures them like a trait theory when it isn't supposed to be so if people are just trying to be as intuitive as possible (lol) send them off to MBTI to have fun there. (I guess you can measure how well someone fits a type or other intratype differences as traits and MBTI lives in that limbo which is why it gets crossed with Big 5 and other trait theories as well as other type theories.)