I don't think its about protecting kids from losing, or from feeling like "losers". For me its about recognising when a player or players (or a team) are getting disheartened, and working out how you can keep them engaged in the sport. The objective from mini-soccer to youth, as its first principle, must be to keep kids interested. If you keep kids interested, they will turn up for training as well as for matches. They will be outside running around and not permanently stuck on their phones/xboxes/playstations* (*replace with indoor-based electronic device of choice). A positive side effect of that will be that some of those kids will be really keen on football. Some of those really keen players will be actually quite good. Some of the players will improve significantly. Some will progress to county football, a tiny tiny minority will be signed on to professional clubs' academies. Others will keep playing up to and beyond the legal drinking age, and become our nemesis on a Sunday morning. But by ensuring kids don't become disheartened through their formative years, we keep the game alive. And this can be done by balancing leagues as best can be done, and not by other artificial constructs such as shortening a game midway through, or reducing the opposition size to below that of the team being beaten. Playing for 60/70/80 minutes and being beaten 3-1 is a great losing scoreline. Being annihilated 18-0 is painful. Enduring that loss week in week out is wrong, and does no favours either to the winning team or to the losing team.
A long rambling post that would be better posted on a coaching forum I think. As a referee you have no responsibility other than refereeing the game in front of you. If you have 11 versus 10 and the winning, larger team want to take a player off to even things up, sure - no problem. "Ref, we're losing 15 nil, can you blow the whistle early?"... "Sorry, I have to play two halves of equal length." The time to have agreed a shorter playing time was before kick off" (of course, if they know the LotG, they might realise they can take "injured" players off and reduce the team size to below the legal limit...). If the coach simply takes all his players off and march away - that's fine, report the facts. Feel for them, but don't play to your own set of laws to cater for them.