Hormonal birth control may be more predictable, but it predictably has bad side effects (acne, weight gain, depression, and a host of other symptoms I’ve forgotten). There are also people where it straight up doesn’t work—one of the women to which I’m referring had two kids on hormonal birth control before connecting the dots and switching.
Overall, everyone has their own birth control needs. Most of the evidence I’ve seen has led me to prompt people having issues to consider the copper IUD because it does seem to work very well (when those complications you mentioned don’t show). A surprising number of people have misconceptions about insertion, periods, hormones, and efficacy, so I’m always happy to increase the amount of power people have over their own uterus by making them aware of their choices.
A certain, cynical part of my brain believes the reason the pill is popular is that there are many, many incentives to encourage people to go a route that returns recurring revenue, not helping women find what works best for them. It seems to be pretty common to simply prescribe the pill when people ask for birth control.