I will prefix this by saynig that:
1) I'm typing this on a laptop now and don't feel the urge to throw up or whatever people say
2) I also have a wireless CherryMX keyboard that I keep in my backpack with me, I enjoy them that much.
There are a couple of reasons that I think other people enjoy mechanical keyboards. First, there's the aesthetic aspect. There are so many options for key caps and bodies and all kinds of other things that can make keyboards genuinely beautiful and a joy to see everyday. Second, many people find satisfaction in the sound and feel of mechanical keys (including myself).
For me it's ergonomics. I'm a pianist and organist as well as a programmer/software engineer/sysadmin/someone who spends a lot of time typing. AS such, I've gain RSI, most notibly tendonitis in my wrist and the finger tendons in my forearms. Before I got a mechanical keyboard, this bothered me a lot more at the keyboard than the piano or organ, because part of classical training is the ergonomics of (piano/organ) keyboard playing. Here's what a neutral posture should be:
> When sitting, your shoulders should be relaxed, your elbows at exactly 90 degrees, a straight plane from the crook of your elbows to the first nuckle (top of the hand flat and level). With your fingers curved down and relaxed, they should be at the bottom of a key press.
Two things to note: First, your wrists are hovering. There's no wrist rest.
Second (and super important) that a bottom of a key press is not the same as bottoming out the key. It's the point at which a key will make a note. A VERY important that you try not to bottom out the key or type "through" the keybed, as this is an impact on your joints and slows you down (as well as stopping motion and other things that important to piano playing but not for typing). This generally is not possible on rubber dome or scissor switches, as bottoming out is the signal. On mechanical keyboards (or at least the types that I use, like MX Blues and the Model M I have at home), however, the \click\ is the keypress, so I don't have to bottom out. Instead I just feel la bunch of springs and a light but definitely actionable feedback.
I will also point out that I have not spent a huge amount of money on mechs. My daily driver at work is a $30 Red Dragon K552[0], which is pretty cheap and has served me well for about 8 months now. I'll also point out that I've heard no noise complaints (and I made sure to ask around after a week) in my open office environment, mostly due to not bottoming out (and because one of my neighbors is a very heavy typer and is much louder, along with the Model M two cubicles over).
You can definitely go much deeper into ergonomics with split keyboards and tilts and all kinds of things, but this works for me.
TL;DR I applied my knowledge of piano playing to typing to alleviate my reoccurring tendonitis and a mechanical keyboard helps with that immensely.
[0]: https://www.amazon.com/gp/product/B016MAK38U/ref=ppx_od_dt_b...