It enhances the penetration of products, makes the skin look better, the make up looks better, but I think I wouldn’t try it if the hair itself didn’t bother me that much. (For dead skin cells, use AHA/PHA)
I have “peach fuzz” (mine is light-coloured but quite thick, I don’t know if it’s peach fuzz category :D) all over my lower face and many darker hair at some places and it was bothering me so much I decided to remove it.
I use eyebrow razors after I put oil on my skin, I do it every few weeks. The hair doesn’t grow back thicker or darker but it’s not smooth and not pleasant to touch where my hair was basically thicker. (So the hair itself doesn’t become thicker but it feels and looks slightly thicker since you cut the top thinner part of it.) However I did not regret it, my face looks better overall and I feel soo much better now that my hair isn’t visible (that much).
Afterwards I use aloe spray and a moisturizer which i usually use after exfoliation. Sometimes other soothing ingredients. I don’t exfoliate for a few days. I always use spf.
Don’t do this on inflamed skin, bumps or acne. Always be gentle, make short movements while you hold the skin tight and go with the direction of the hair-growth.
You can learn about it if you search for “dermaplaning (at home)”. I’m not an expert of this, I’ve done it 7-8 times and only with disposable eyebrow razors, but I’m planning to try a reusable tool. Some work on dry skin so make sure to follow the instructions.
P.s. There are other hair removal methods but i think you meant this one. As far as I know waxing is not recommended for many reasons (maybe excepting small areas). Tweezing/threading and others are different topics.