I'm the creator of Gamerzilla. I watched the achievement systems of Steam, Xbox, and Playstation grow. I've heard of people declining to buy from GOG because they want the achievements available on Steam. Open source didn't have a way to counter this network effect.
Gamerzilla is my solution. It doesn't rely on a single vendor's site. You can run your own Gamerzilla server or use one provided by someone else. It is talked about here mainly because I post about it as much as I can. Open source solution tend to take a long time to gain traction. My hope is to eventually get some of the smaller game sites to adopt it. Steam will likely never change but imagine itch.io, GOG, and other sites using an achievement system that allows you to buy your game anywhere.
I think it is better than creating a custom achievement system because it handles the saving and loading for you. People who do want an online site to display their achievements can use Gamerzilla. It does not display anything when you get an achievement so that is still something you will need to implement if you want it. I've dropped some features found in most achievement systems. It does not have hidden achievements and does not record when achievements are acquired.
I've given a few talks on the subject. If you are interested I can dig up links.