I would imagine from a practical point of view that finding a helmet which is comfortable and fits well would be a first priority as with anything that you might expect to have on your head for several hours. (I'm not making any arguments for or against helmets). It would be a bonus to have something like an action camera moulded into it without either making it too bulky or affecting the comfort or impact absorbing ability of it. The thing is that for all its bulk, a cycle helmet is quite a light item, and concentrating a small dense item like an action cam somewhere in it could be very difficult to do without compromising the helmet's basic function.
You could have a very functional helmet. You could have an effective helmet cam. Can you combine both without one degrading the function of the other? I don't know. It's possible that having one attached on a bracket that allows the camera to pop off on impact (should the worst happen) without imparting any impact to the helmet, maybe on a lanyard, could work.
I did try a budget camera at one stage but I used it on my bars. It seemed a nice idea to record the pretty part of some of my rides. However, although I managed to get it to work I found myself stressing about whether it was recording, had it turned off, did the battery have enough charge, etc and I found that it was spoiling the spontaneity of my riding experience. I wasn't setting out to be Biking Mikey, and maybe modern ones are more fire and forget. Riders do get them to work successfully, but for me it was another annoying thing, like an over complicated bike computer, that sneakily stole my pleasure while setting out to add to it.
Sometimes, more is less, and vice versa. Adding something like a sun visor is very cost effective. You could make one yourself, and stick it on with double sided tape. Some nominally off road designs have them moulded in. The big thing is, needs no batteries! Don't have to set it up with your mobile phone.
