Slackware Linux does precisely that.
I'm a Slackware user. Slackware does have a package manager that can install or remove packages, and even a frontend that can use repositories (slackpkg), but it does have manual dependency resolution. Sure, there are 3rd-party managers that can add dependency resolution, but they do not come with the distro as default.
This is a very personal opinion, but manual dependency management is a feature. Back in the day, I remember installing Mandrake Linux 9.2 and activating the (then new-ish) framebuffer console. The distro folks had no better idea than to force a background "9.2" image on framebuffer consoles, which I hated. I finally found the package responsible for that. Removing it with urpmi, however, meant removing all the graphical desktop components (including X11) because that stupid package was listed as a dependency of everything graphical.
That prompted me to seek alternatives to Mandrake and ended up using Slackware. Its simplicity had the added bonus of offering manual dependency resolution.