Requiring helmets begs the question of appropriate design, which ALSO takes time and money. I don't think anyone in their right mind will want to suggest wearing a football helmet for lacrosse.
The helmet experiment in the pole vault may be a good lesson here. People who didn't understand the physics of the event tried to demand helmets due to the danger of hitting the standards. First, properly trained and supervised kids do NOT hit the standards. Second, the presence of a weighted object (i.e. the helmet) changed the way kids held their heads during flight, thereby changing the way the brain moves around inside the head. There is now the danger of kids breaking their necks due to the extra weight, so many areas are backing WAY off the requirement, which never got all that far in the first place. I've only seen one kid wear one in competition, and it seemed to hold him back.
Other sports? Maybe. But I'm not convinced. For sports like lacrosse and field hockey, EVERY player requires a full field of vision, unlike a football lineman, who really only needs to see right in front of him and perhaps a little more. Once you put a helmet on someone, the next "logical" step is some sort of facemask. For a sport like lacrosse and field hockey, IF you go there, it should be similar to the hockey face shield, not the football crossbars, but most people are only familiar with football. You're going to get a bunch of things added to the rule book, like facemask penalties, which will have to be called to a great degree at low levels of competition, which will break up the action and impede player development.
I don't like this at all. Sorry I wrote a book here, but I think the idea of bringing helmets into every sport is asinine. Next thing you know, Tiger Woods will have to wear a helmet because of the remote possibility that Phil Mickelson's tee shot will knock him out.
