Security personnel quality is HIGHLY variable. So no, they're not necessarily going to be the best people to handle the situation. But that IS the job.
Even with highly-trained off-duty/former cops, the same issue arises, though. They have limited time and investigating an incident perforce means they're not preventing other ones.
But, there's the issue right there.
1. FLGS's most certainly won't have security. So, the person who has to deal with any complaints is likely the manager/owner. It's simply not his job to assign blame or determine the truth. It doesn't matter. His job is to find a solution that won't cost him business and makes everyone as happy as they can possibly be in this situation.
2. Most Con's are too small to have actual security. Sure, Gen Con or whatnot, where you have thousands of attendees, fair enough. But a local con with a couple of hundred attendees? Not a chance. Plus it's not a security guard's job to investigate. That's not what he's there for. He's there to provide security. By and large, any complaint of harassment isn't going to be handled by a security guard, it's going to be handled by the Con manager(s). And, again, their job is not to assign blame or determine the truth. Their job is to make the Con go smoothly and make everyone as happy as they can possibly be in this situation.
Expecting them to track down witnesses? Good luck. Not going to happen. Reviewing security tapes? In the middle of a convention? Again, good luck. It's just not going to happen.
So, you put a policy in place that is general enough to allow the manager to have some lee way to determine courses of action (i.e. zero tolerance policies are likely not the answer) but, are also strong enough that action will be taken.
Again, the most likely course of events is that a complaint is made, the manager goes and talks to the person, and informs him or her that a complaint was made and that he or she should cut it out or they will be asked to leave. Does it suck if it's just a misunderstanding? Sure. That blows. Again, most Con's are small enough that if it was just a misunderstanding, the accused can just apologise to the person who felt harassed and that will be the end of it.
By and large, that will be the end of the majority of issues. Just like any other public venue.
Personal anecdote time. I'm on the staff of the local Teacher's Association. We get together every month for training and seminars and afterward we all go out for dinner and a drink. Fifteen, twenty people usually. I received a complaint after one night that someone had said something offensive. My first response was, "Was it me?" ((I can be kinda loud, boisterous and opinionated... the hell you say?

)) but, no, it wasn't me. And names weren't actually used. Just that someone said something that was offensive. So, I took this information, had a quiet word with everyone, not pointing any fingers, not accusing anyone of anything, that maybe toning things down and being a bit circumspect in their humour was a good idea. Problem solved and everyone, AFAIK, is happy.
THAT'S how the vast majority of harassment issues are handled. At least, AFAIC, how they should be handled. The point of a harassment policy isn't to punish harassers.
The point of harassment policies is to stop harassment.
If the harassment stops, job finished and everyone goes about their business. These ideas of punishment and whatnot, that's for the police and lawyers. Someone making dead baby jokes at a game table isn't a criminal. There's no need for police to get involved. But, there is need for the community to tell that guy (or girl) to tone it down and watch what they are saying. All this other crap about the need to get the
truth is just missing the forest for the trees. The point of these policies is to provide a space where we can all be together without having to deal with other people's crap.
En World is proof that these policies, when enforced, work perfectly well. No one involves the police over Modable statements on En World. There would be no reason to. But, we certainly can report things to the Mods and have a reasonable expectation of action being taken. That's the way things should work in the real world as well.