I use Linux Mint and occasionally I have to compile things from source because somewhat old binaries can't do what I need them to. Would Gentoo actually be a huge improvement over the status quo?
It really depends how much you compile. And what you want.
I want a rolling release. And I like having a package manager take care of the updates, instead of me having to remember and deal with it, outside of running a couple commands, and taking care of my entire system. I also like having a lot of control over what I'm using.
If none of that is important to you. Or you don't want it. You shouldn't use Gentoo, you will probably not have a good time. Also if you aren't alright with having to read the manual to figure out how to install/get things working. Again, it's not going to be for you.
There is a reason it's. Not the most used distro, but there is also a reason the people that like Gentoo, generally really like Gentoo. It does the niche thing they want it to do.
My advice, if you don't like the idea of some of the stuff involved. Don't care about use flags and all of that stuff. Use arch. Aur helpers don't have as much control, but if you don't care about use flags anyway, that doesn't matter. It will take care of updates for you. And you probably won't even need to really use the aur, if you just need actually up to date packages. Since the arch repos, give you that without even needing to compile packages.
Also if you minimize packages from the aur, it's a very stable os actually. A lot of people have wierd issues because they just install pavkaged from the aur, and other places without thinking about what they are doing. So some update happens the aur packages aren't using the right libraries anymore, like all of the normal repo packages are, because arch wont update a particular package until everything else in the repo is able to work with the new packages. The aur stuff doesn't get the same treatment because it's not officially maintained like the actual repos are. So if you happened to install a package that doesn't have a maintainer, or one that is slow to update. You can end up with broken packages. Or if you are using git packages, and you don't have git versions of dependencies that the package needs that will cause issues too.
So basically arch breaks because retards don't think about what they are doing.