To the best of my knowledge LARP games, including those Belegarth psychos, are consistently very safe. This is all annecdotal of course, but I'm going to offer it up anyway, because I don't have numbers.
With a football team, you've got 30-60 or however many kids they put on those things, running around every day, lifting weights, training, slamming into things, slamming into each other, falling down, getting thrown, whatever. They train five days a week and play a game, so they're got something like twenty training days and four game days every month, and every one of those days is intensive physical activity involving active grappling, tackling, and throwing, all the while wearing disgracefully poorly designed armor and not using shields.
With any given Larp, you've generally got one game day a month, and between one and four practice days. Instead of one 200 pound kid charging pell-mell into another 200 pound kid at full bore you've got people whacking each other with boffers or rattan sticks or whatever. So immediately we're down from 400 pounds charging at a combined speed of 20 miles an hour to something like .5-2 pounds, still going something like 20 miles an hour.
On top of that, the guys who really hit each other (Belegarth excluded, they're crazy) typically wear rigorously, even anally, safe armor, Consisting massive steel helms, gorget, kidney belt, some kind of crotch protector, full knees and elbows, generally with wings and associated greaves and cannons, and so forth. Hell, they even wear gauntlets. When was the last time you saw a foot ball player wearing gauntlets?
And on top of that you've got a lot of safety conscious players and martials who will call a Hold if they see a dangerous situation, and a lot of players who will drop whatever they're doing when someone calls hold, which you really don't get in most sports.
So, the Larpers tend to have better armor to protect them from much less severe impacts, they're usually more concerned with safety than screwing up the play, they're not throwing or tackling each other, they're using shields, and instead of trying to bodily hurl someone out of the way they're trying to strike them with a weapon that can 'kill' with relatively little force.
My point is that what is considered 'safe' for a seventeen year old kid is a lot more dangerous than what Larpers put themselves through. I've been told time and again that SCA, Bel, Dag, and Amtgard have very good relations with their insurance agencies because they have very low rates of injury for a physically active sport.
I should also point out that each of them insists that the way they do it is the safest. SCA just has to have 16 gauge thick helmets, no matter that that's several gauges thicker than many medieval examples and might just be adding unnecessary weight. Amtgard swears up and down by their pool noodles, various groups are quite happy with every kind of insane scheme for making safeish arrows, ranging from carbon fiber arrows with rubber blunts to tennis ball shooting croosbows. The Belegarth guys, who are quite happy shield bashing from a ten step charge, balk at the idea of having siege engines for fear of someone getting tangled up in the mechanism. The SCA play with trebuchets but would pop a rivet if you suggested legalizing shield bashing.
At the end of the day I don't think any of them are basing their rules and practices on a clear headed scientific evaluation of what is and is not 'safe'. A lot of it just seems to be tradition, and once it got into the books it stayed that way. It's like Padded or quilted armor in D&D. A 30 layer thick padded Jack has been shown, in experiments (Check Myarmoury.Com) to be very effective at protecting from cuts and some stabbed, but you only get one point of armor for it in D&D? Why? because that's how it's always been!
Upon consideration, I have decided that the Larpers of America should get together and make some sword testing robots. One would repeatedly stab a sword into a block of ballistic gelatin until the tip failed, another would whack at a bit of platemail backed by ballistic clay until the core failed, and another would shoot different kinds of LARP arrows hundreds of times while volunteers carefully track the results.
And like you said, there's other LARPs out there that allow them. That's why I attend those over Alliance whenever they fall on the same weekend.
