You don't actually HAVE to use phi. That's just the default global scale factor. You're correct that it's kinda marketing spiel. I figured I needed an angle to stand out in the crowded design system world and now I'm paying the consequences in this absolute roastfest, lol.
The only real reason I use phi is because it's very useful in asymmetrical typography scaling. At small type levels, differences in font size are more visually apparent than at large sizes. In other words, 14px vs 16px looks more noticeable to me than 38px vs 40px. So, my goal was to find a rem coefficient that would provide large jumps at large sizes, but I could also use the square root of it to derive smaller increments. I tried phi on a whim one day and realized I liked it.
I also went to apple's HIG and looked at the type specs for MacOS and put them into a spreadsheet. I found that the proportions of line height to font size hovered around 1.272 (which is the sq root of 1.618, or phi). Then I found similar patterns in the ratios of difference font sizes to each other (I think. It was back in 2022).
I also did a bunch of personal tests where I'd try to eyeball line heights and padding and stuff without snapping or looking at the metrics, and my preferences kept landing around golden ratio proportions. Biased? 100%. But I haven't got access to focus groups, and every time I asked my boyfriend to try it for me he'd be all like "please get a job you promised you'd work on your resume today"
So then I looked into other research. I can't find the study because I unpublished the article where I linked it, like a dumbass, but studies have shown that laypeople can tell the difference between abstract art based on rules like fractal symmetry and the golden ratio versus art made by children or animals at a rate of about 60% accuracy. Im on my phone right now but if you're curious I'll gladly look it up for you. I took that to mean "well, if we're entering an age of AI generated interfaces, then eventually we'll need to distill the essence of what looks good into certain mathematical principles so that there's a quantifiable "baseline" for quality that models can rely on. Golden ratio!" (Note: I do not know how AI actually works)
Finally, I got obsessed with that damn material button. There were ads on BART for some Google thing showing a button and it just looked off center to me. It haunted me for weeks. I couldn't stop looking at it. So I thought I'd try finding a reliable way to achieve the correct optical offset, but programmatically, so a designer wouldn't just have to do eyeball every button every time.
So, it's not totally baseless. But it's not a magic number either.