I DO use outposts as often as possible when I find a good location for them. I always use a captured worker to build them, though and it takes three turns instead of one. Any mountains in your territory that are three tiles from a rival city are good locations for outposts, since they show you at all times the best defender guarding the city.
But yes, according to the mini-manual outposts are supposed to let you see four tiles away on a mountain, three tiles on a hill, and two everywhere else, but it's really three, two and one... resulting in NO extended vision at all on flat terrain... probably an error that needs to be fixed.
They are also useful on coastal mountains on the very edge of your border or just outside of it to give you a nice view of the sea and ocean beyond.
What is a unit's field of vision on a mountain? Is it not two tiles away? While the vision with the outpost is three tiles away. I disagree with the unit being able to see as far as the outpost.
Any outpost that gives you an expanded view of a rival's territory is indeed useful in wartime, but yes, they do need to be protected.
The thing I hate most about them, though, is they are automatically destroyed if an enemy unit takes the tile they are on. I think the enemy should first have to occupy the tile then pillage just like any other improvement. Any out post you have is sure to be targeted in war.