aa777888 - yes but professional mitigation of those risks helps reduce the odds rather markedly.
@crab and @Bell_ringer: let's face it, as far as the both of you are concerned, the only safe way to fly tours, short form or long form, would be in a twin. Because short tours typically occur at low altitudes over congested areas, and long tours (e.g. Grand Canyon, Hawaii, etc.) often occur over forbidding terrain. However a twin would make the business case infeasible (nobody would pay the required price), and in many cases the use of even a single engine turbine ship the same. This makes that part of the industry a substantial province of the venerable R44, which you both seem to feel is hopelessly inadequate to the task from a passenger risk perspective given the typical flight profiles.
And yet, from a strictly US perspective, both the passengers and operators would appear to disagree with you. Leaving aside the recent pandemonium--er--pandemic nonsense, the industry does a booming business, and the short form, piston-powered subset would seem, admittedly anecdotally based on media reporting, to do so more safely than the single turbine, long-form part of the industry.
As someone who has done quite a bit of the short-form, and a limited amount of the long-form, my impression is that the average US short-form customer desperately wants to risk their lives, they want the "thrill ride", or at least the impression of one. They have no illusions. I can't tell you how many times I've been asked to do aerobatics. Alas, my standard answer is "This is not the Red Bull helicopter." Throwing in a few mildly steep turns is enough to have them asking for a few Kleenex to clean themselves up with, and I don't mean vomit. Thus maintaining the illusion and not the reality of danger which, of course, is vitally important. Meanwhile the long-form US passenger prefers a limousine ride, even those who want to shoot "shoe selfies" (none of my passengers, thank goodness).
At any rate, in the US it's not the FAA that controls this business sector, it's the insurance industry. I'm proud to say that the operation I'm associated with still enjoys low enough rates, even with the recent departure of several US underwriters and substantial rate increase across the board (thanks so much, certain HI and NY op's), to make the venture profitable. This is even in the face of underwriter representatives showing up at one of our events to monitor operations, something which we welcomed wholeheartedly.
I hope you find the preceding discussion professional enough, because I and those I'm associated with certainly approach the business with a very professional attitude toward both business and safety.