Personally I've not had a lot of noise out of my '16 (yet) and I really wouldn't get too concerned if I did get some cam chain noise personally. I also have a '14 ZX10R and a couple of ZX6Rs. Both of my ZX6Rs would get pretty noisy and my '14 ZX10R is much worse than my '16 at the moment. But, you have to expect a certain amount of noise from a ratcheting type cam chain tensioner.
It should be the quietest right after it auto-adjusts to the next click, and that is the point when the tension should be at it's "optimal". As the guides and chain wear the tension will get lower and lower until which point it's low enough for the tensioner to click another notch. During that time the chain will get a bit noisy, and not necessarily bad mechanically, it's just annoying to the ear and it "sounds" like something is wrong when it might not be. One thing people do that is a very bad thing and shouldn't be done, is they back the bolts on the tensioner until they hear the next click and then tighten them back up. Sure, it stops the chain noise, but it also puts too much tension on the chain which at best will cause things to wear faster than they should. I put manual tensioners in my ZX6R so I could fine tune the tension. Manual tensioners are infinitely variable where the OEM ratcheting type adjusts tension in increments.
Having said that, I believe the OEM tensioner has a tendency to stick, and not adjust when it should. When that happens you should pull the tensioner completely out, clean and lube it with oil and verify it's working then reinstall according to the manual. The chain may still not be at the point where the adjuster is between clicks and still making noise, but it will be adjusted properly.
In your case, the dealer replaced the tensioner with a new one and it is still making chain noise and I would say there are 2 likely reasons for that. 1) The chain is between clicks on the tensioner and is normal noise, confirmed that both your old and new tensioner exhibit the same amount of noise or 2) the noise is completely unrelated to the cam chain tensioner and possibly unrelated to the cam chain.
It's hard to accept that some noise coming from the cam chain area is "working properly" but that certainly can be the case. Hard to say without hearing it in person.