hand it over to them is CLEARLY out of field goal range already, why not go for it on 4th down, rather than kick away one of your possessions at the end of the game.

Earlier in the game that's different, as field position is more important, and you can make it up later if they score points because of a short field. But later in the game, possessions trump field position, when you're in a DO OR DIE scenario. Whether down by 3 points or 7 points, I'm not sure why coaches decide with 3-4 minutes to go to punt it away based on the concept that they "trust their defense to get them the ball back." It's faulty thinking to not instead go for it on fourth down, IMO. If you make the 1st down you're in business still, with plenty of time, all your time outs, and a defense that's now on it's heels. If you don't make it, you've still got to stop THEM from getting a first down to get the ball back, whether its on their own 10 / 30 / 45 yard line after a punt, or your own 45 / 35 yard line after turning it over on downs.

Even if you turn it over on downs at your own 40 or 45 (35 for some kickers), that defense you're "trusting" stops them 3 and out, you get the ball back, but if the defense allows 2 or even 1 first down, it's probably game over anyway, no matter where on the field the other team starts their drive. Now, if they are within FG range for their kicker when you turn it over on downs, that's another story. But otherwise, always go for it on 4th down, and you give yourself two chances as opposed to kicking away one of them. You may still get that second chance after stopping them (hopefully 3 and out), but you've kicked away the other possession that may have been the game-winning drive.