They grow heavier over time if not used and will dent your foot more if dropped.
If it's just dusty that's not necessarily a problem. If it's got mold or corrosion that's more of a problem.
The meter may be dead (not necessarily) but this is not a show stopper. The unmetered prisms are more compact but often have somewhat of a collector's premium price, so if you just care about use value, waiting for one also implies paying more.
The shutter of the F is generally very reliable and though any shutter can fail, that would not be my first worry. If the camera and lens have sat for a long time, my first concern (apart from battery corrosion) is for stuck or sluggish lens aperture, focusing helical, or fungus in the lens. IME, 50-year-old Nikon lenses have slow apertures less often than some other brands, but it does happen and I have a couple of examples.