Steve, I'm sorry to be pedantic about this but I have a bit of a thing for hot nav skills..... so...
The fog you describe didn't just switch itself on like a light, as the fog comes in then so you make your current point the waypoint you work from (so you do know your current position). If you went out from the start in the fog then the start point is your first way point. Either way you will always know where you last were and were you are now, as I'm sure you'll agree this is elementary in whatever you are doing in the mountains. You clearly have great experience in the mountains so you will have noticed the fog coming in and prepared yourself acordingly. Had you carried out the pinpoint nav skills that Chris talks about below and you clearly are more than familiar with then you would have had no need of the GPS to tell you were you were at any given point along the route you have taken.
Imagine a situation with somebody in the hills who has a GPS but doesn't have the same traditional skills you and I have, they aren't watching their surroundings, keeping tabs on the weather, their last waypoint (physical rather than gps) and concentrating on the route ahead, maybe they missed the fog coming in so fast because they had their head down scrutinizing the GPS waiting for a full SAT lock...the next thing...bam, they are in your position, the fog has arrived...and just at that point the SAT's go offline, the GPS batteries run out, the walker trips and breaks the GPS or any other reason why these things break and usually when you need them most. Now you or I could Navigate safely off that Mountain still, albeit rather slowly and painstakingly... but could the lesser skilled walker?
Don't get me wrong, as I said below I have one and it lives in my bergan... Had I been in your position I think it fairly likely that I'd have got it out and used it as you did....but only for speed, convenience (last orders and all that

) and for the fact that I could because it was there. Had I been in your position without it, having the skills we have would have meant it made no odds to me one way or the other. A few extra hours as the going is a little slower but the same end result. And I'd also venture to say that had I been using my map and compass and awareness of my surroudings I cannot see how I would have got into that situation in the first place.
This is maybe what I mean about not needing them as a backup and the importance of traditional skills....
I don't think any of us disagree on that... in short, as you say handy and convenient but definitely not nessarsary...and in extreme cases...possibly dangerous... :biggthump