Most kids see them for what they are and discount their value appropriately.
But for a couple kids they do represent accomplishment, and it's not all bad.
I remember a 12 year old on a LL minors team I coached many years ago. He had no athletic ability. None. Weak, immobile, and timid, he could not bend, stretch, run, throw, or hit. His parents were extreme sedentary types with no clue about anything to do with sports, fitness, or movement. Two or three years older than the other players, this boy was by far the worst player on the team.
With the parent's consent, I obtained a waiver of the league rule requiring each player play a couple innings in the infield. It just wasn't safe to put this boy in the way of a batted ball. The board was skeptical until one of them watched one of our practices. He quickly convinced the rest of the board.
This boy had never had a legitimate hit in his previous years in the league, and I made it my mission for him to get one that season. I told him never to bunt and never to take any pitch he thought he could reach. Regardless of the game situation, his job was to take three hacks every time he came up. Ignore everything I taught the rest of the team about pitch selection, count, and the strike zone. Don't even look for a sign. Just swing.
He put a ball in play for the first time about a third of the way through the season. In the succeeding games, he had several medium-strength groundouts and reached on errors a couple times. But that first hit eluded him until the next to last game of the season, when he rapped a clean ground ball single through the 5-6 hole. Unfortunately, he reverted to form and went oh-fer in the final game.
When we handed out the league-supplied participation trophies at the team party, it was clear most of the kids knew the score and were in no danger of receiving an unwarranted self-esteem boost from them.
My one-hit wonder hitting pupil, on the other hand, positively beamed as he shuffled up to receive his trophy and eagerly grasped for it with chubby hands coated with pizza grease..
There was no way any trophy could make this boy soft. He was already as soft as a boy could be while still claiming to be a vertebrate.
And there was no way the trophy instilled a false sense of ability. He wasn't stupid. He knew was awful at sports. But the trophy had value to him. It might have been the first thing he ever worked for.
Maybe some day, the memory of it will help him motivate himself to become a little more active as an adult.
I love that story! I have coached several of my kids' teams, and I have had players with similar abilities as the ones you described. Having the kids follow through and complete the season is something that should be rewarded. I just don't see the problem with handing out a participation trophy for the Rec League Teams.
At the end of each season, when the participation trophies are handed out, we would always talk for a moment about each individual player. Several times a player's parents would come up to us with tears in their eyes and thanking us for the experience their son had. Handing out a trophy could help to keep the fond memories of their experience. I don't think it hurts at all.