Why waste time and duplicate the efforts of LineageOS? They've probably already got enough work maintaining F-Droid as it is, without having to add an additional Android fork (and never mind supporting a variety of devices) on top.

And at the same time, the target audience interested in installing a custom Android fork would be much smaller than the potential target audience for F-Droid in its current form.

(Also, for the time being, a much more minimally invasive and less resource-intensive approach would be some sort of Shizuku-like approach, i.e. using the ADB network interface originally intended for wireless debugging.)