Putting the wind on your tail will always give you more choices of where to put it down.
I agree with most of your statement, except that.
A tailwind from one thousand feet is not at all the same as a headwind from fifteen. A small airplane with a sixty knot glide speed and a five hunded foot per minute rate of descent in that condition (assuming no other changes with altitude) provides a 50 knot airpane traveling forward into the wind for 30 minutes, or a 70 knot airplane traveling with the wind for two minutes.
In either case, the airplane at fifteen thousand has a decided advantage, particularly if he or she elects to fly with the wind rather than against it.
As others have correctly noted, however, achieving a safe touchdown is the goal, as opposed to merely traveling as far as one can possibly go. If one is flying that single engine airplane properly, one has kept a suitable forced landing site underneath for the duration of the flight, and knows where it is long before the power has failed.