Alpine is uclibc/busybox, and can be used as a desktop IIRC. Tiny Core is glibc+busybox. Aboriginal is uclibc+bb, but doesn't do X IIRC. Gentoo can be configured like that. Etc.
I do wonder why, if your target is a desktop, the bloat of glibc and GNU utils even registers; surely the bloat of firefox exceeds their combined bloat 1000-fold? Even the bloat of Xorg is a lot when compared to tinyX, but you still want the acceleration for desktop use.