You're right that the tech depends upon power & signal. I always carry paper maps and a good compass, although find that they're used less and less frequently. Although my Montero has a built-in compass (and I swing it occasionally and correct it for declination as I travel), I use the one on my GPS more than anything else.
What would you use a dash-mounted compass for? If it's just to have a rough idea of which way you're pointed, that's fine, although the sun (when available) can tell you that and space is at a premium on most dashboards these days.
If it's for anything approaching accurate navigation, you're going to need a good handheld and will have to take it away from the vehicle.