I'd been scrolling through the comments, contemplating sharing my own "dish soap" story, when your comment and the one above both inspired different anecdotes. So although I'm responding to you, I'm just going to go ahead and tie all these topics into one post:

My hair is like yours. I'm a woman (though I don't feel right saying "cis," since I don't really "get" gender) and have very fine hair on a very oily scalp. Like you, I cannot go a day without washing my hair, lest I encounter issues. 24 hours without a wash is obvious, by sight, by touch, and possibly by smell (if you were to get close.) I wish people would stop spreading that no-wash "advice" as if it'll 100% work for everyone of every hair/skin type. For some of us, it can actually make problems worse.

I also had a time where I was losing my hair (unrelated to hygiene.) It turned out to be a hormone thing - but not in the way the above commenter hypothesized it would. My estrogen levels were low, which meant my testosterone levels were relatively high. Rather than fortifying my hair, testosterone was making my hair thinner, and the result resembled male pattern balding. Thank fuck, going on an estrogen pill managed to correct and even reverse most of the damage. (Though now I fear the US government trying to take away my birth control, which is actually "magical hair maintenance pills" in my mind. But that's another topic for another day.) Either way, hormones absolutely play a role in hair. Pregnancy and its cocktail of hormones is well-known to cause changes in hair thickness, texture, and even color. However, there are too many variables to precisely pin any one particular effect to any one particular hormone across every single person. For me, estrogen vastly improved my hair. Others' results may vary.

As to dish soap, I was around 11-13, middle school age. A (female) friend had said she used dish soap instead of shampoo. I was curious and decided to try it. It worked to wash my hair all right, but my hair didn't feel the same afterwards. It's hard to recall by now exactly what was different, but there was something about the resulting texture that was off. I've tried a number of different types of shampoo throughout my life, but every single one of them provided a certain result that dish soap couldn't provide. So although it might suffice for some people, I'll have to add "dish soap as shampoo" to the "things that personally don't work for me" box.