I also shoot events as a part of my business.
And, from my own personal and biased point of view, yes, of course I'd like to see more restrictions on photography. But, I don't demand it of organizers and I am pleasant or even helpful to amateurs and parents shooting alongside me. (Note: In most cases I do require that I'm the exclusive commercial photographer authorized to shoot the event, but that's another matter.)
However, there are a number of very good reasons for event organizers to put restrictions on photography, besides my photo business success.
Safety is a key one. I've just seen too many people wandering with their cameras into places they shouldn't, and causing problems that could have been avoided. I've seen people use flash when they most certainly shouldn't (and I'm not). A single, professional photographer is less likely to cause problems, especially if they know the sport or event well, know when and where to go, and are well versed how to shoot it safely and without disruption.
Another consideration is kids... Whenever they're participants in any event, an organizer has to be concerned about exactly who is in the audience taking pictures and why. Pedophiles are the first thing that comes to mind, of course. But also consider the booming business of micro stock and royalty free images, and the amateur photographer market that feeds it. Any image might end up anywhere today.
Both the above go toward liability. The organizer has to think about that, and needs to minimize their own risk, and that of any sponsoring organization. And, when the lawsuit happens, it will be the deeper pockets of the organizer, the venue and any sponsoring organization that will be named co-defendants along with the amateur who they allowed to take the photo, or who caused injury by being in the wrong place at the wrong time.
Also, an organizer needs to put on an orderly show without disruptions. In many cases that means the audience sitting in their seats watching. If there are a dozen parents up and wandering around in front of the rest of the audience during the show, angling to get that "perfect" shot of little Johnny or Suzie, the rest of the audiences' viewing and enjoyment of the show might be obstructed.
Now, you might scoff at the above points and rightfully say that you'd never cause any problems. But, how does the organizer know that? You might even say you've never seen any photo-related issues at any event you've personally attended. But, it only takes one or two in a hundred - maybe even one in a thousand - to create some serious problems the organizer will have to deal with, perhaps even to the extend of threatening the organizer's business. Problems that could easily have been avoided, by restricting photography.
Yes, I do sell some photos to people who are at events with their own cameras. Some serious amateurs toting D-SLRs ask me how I managed to get a particular shot and end up buying from me anyway. In fact, serious amateurs are often the most appreciative of the shots I display at events, and make a lot of positive and kind comments. The P&S crowd sometimes are disappointed with their results and end up my customer, too. The camera phone user... well, let's not even go there.
However, it does effect sales very noticeably. Maybe some are embarrassed to admit that they didn't get a decent shot (sorta like stopping by the market to pick up a couple trout after an unsuccessful fishing trip). Or there's stubborn pride that "they can do it" and "there's always the next time". Or, perhaps it's just that since they were shooting, they didn't bother to make a purchase onsite, or to pick up my business card or brochure and don't' know where to find my images online.
Sometimes it's even more dramatic. One of the least profitable events I've shot this year had a proud Dad wandering around with a brand new 1D MkIII and kit of L-series lenses. He was not only photographing his daughter's participation, but everyone else's daughters and sons, aunts, wives, nephews and mothers, too. And, worse, he was offering free reprints to anyone and everyone there! He was snapping away at 10 fps and odds are got some good shots, although his editing and post-processing must have been a real nightmare! (I took about 700 shots, I would have estimate he took at least 5 times as many.)
Now, this guy can afford to buy photos. He's a lawyer in one of the most affluent counties in the U.S., driving a bright yellow Hummer H2 towing a $25,000 horse trailer with two $25,000 horses in it, along with tack supplies and several $500 costume changes for his kid. (Hey, maybe I should show up on his office doorstep, greeting his clients and offering free legal advice - just my opinions, of course, since I'm not an attorney - and handing out info about Nolo Press or any other DIY legal resource I can think of.)
A good organizer wants to provide a suite of services, including photography, to his "customers": the participants and their families. So the organizer needs a photographer who will commit to doing the job, show up on time, stay the full day, get good shots of all the participants and handle everything professionally. They need someone who will not only be at this event, but also the next one and the one after that, and whose work they know and can trust.
Amateur photographers run amok may or may not be there week in and week out to take the photos, may or may not produce usable photos, may or may not get shots of all the participants, and, most certainly, will undercut the sales of the pros hired by the organizer.
With profitability gone, the pro photog will either stop contracting to provide services at that organizer's events, going elsewhere in search of more profitable business, or keep trying but go out of business for lack of sufficient sales. The professional photographer has a large investment in equipment and time, which they need to get a reasonable return upon, or they'll simply have to look for other work. Either way, the organizer loses an important resource.
Does this really happen? I can assure you it does. A venue I was at a week and a half ago asked me if I knew a videographer. Theirs had canceled on them. Just too many people were now shooting their own videos, making it unprofitable for the guy to come and serve the other participants.
Also, an ongoing, working relationship between the organizer and photographer can provide a sure source of images the organizer will need for future event promotion or other marketing efforts. Amateurs who just happen to show up at a show or two and shoot only portions of the event are not a very reliable resource for this sort of thing, either.
So, for the long run and consistency, for safety and out of concern for kids, plus for their own liability and to protect one of their resources, an organizer has a lot of valid reasons to restrict photography, besides the most obvious and selfish appearing ones.
Over the years, experienced organizers have seen all kinds of pro photographers at their events, and value a good one whom they can trust. So they tend to be supportive of them. I appreciate that and reciprocate as best I can... And I somewhat dread the other kind of "organizer" (i.e, the volunteer parents committee).

. Seriously, that's just competition even if it is a parent shooting. Just because a person can afford the photos doesn't mean he should be ripped off at $40 a pop for 4x6 prints (which is what I've seen some charge). Photogs who do this are getting the competition they deserve in my opinion.
