Yes having a winch gives me the feeling that it will bail me out of a situation...because it does. Multiple times I've come up to a single obstacle on a trail, gotten stuck (too much or bad line, whatever). Pull cable, gotten over it, cleaned up, kept going. If I didn't have the winch, I would have been extra screwed.
My dad used to say the same thing. Then we were out on some property, we were going down a single track when we had to turn around, he said back into this wee tiny clearing. Little did we know, it was super soft and the truck just sank. The front tires were a foot from solid ground. Pulled cable, got the truck back on the good ground, went home. What could have been a super ordeal (stuck for at least the night, possibly longer if we had trouble on the 4 mile walk back...to a phone...not help, a phone) was a 15 minute inconvenience. He was a fan of that winch afterwards. We used it a number of times for rescuing others and moving heavy items.
Also I disagree with "you don't need line speed". Yes. You do. A few reasons: 1st off, if you are recovered faster, then less wear and tear on your winch. Sounds counter intuitive, but what kills winches is holding that button down for long periods of time. Slow line speed, you are winching longer. Faster line speed, done. Also you get recovered faster. Less time being in a jam. Lastly (and can actually be important) is proper trail etiquette. By not being stuck for 2 hours because your POS winch is slow and burned out the solenoids, you are clearing the trail, and moving on. I've seen many times when guys had slow winches and they took FOREVER to clear out their rig. Like...and hour. The fast winch guys were out of the way in under 15 minutes, easy.
Not saying you need to go trick out your winch, but a fast stock winch is the way to go. Yes the faster ones are more expensive, but you can buy used and rebuild them (if needed, most winches are hardly ever used) to offset the higher cost.