The question you ask in the title is a more general one that you ask in the title.
Yes, Gentoo is a good choice.
No, it is not worth compiling every package. This should not be the main reason you choose Gentoo.
Admittedly, I started with Gentoo for the same reason (per-package compilation), hoping for performance gains. However, I stayed because of the excellent documentation, the great user community; the rolling versions; the customizability and control I have over my system, the choices I need to make when installing, and keep making as the install is continuously set up over the years.
I’ve tried quite a few distros over the (+20) years of Linux-use. I keep choosing Gentoo.
I’ve heard good things about Arch. Indeed, I installed it on one of my boxes, where I specifically wanted to avoid a lot of compilations, besides being curious about it.
Used it for a bit over a year know and… I don’t know, it hasn’t been as stable, and I’ve find using AUR more of a chore than custom ebuild repos. It’s probably great when you get used to it, but so far I still prefer Gentoo.
It’s great, that there are several good distros for different use cases, and that we have the freedom to choose what suits us best!