I've owned and used them in the past and they can't be beat for convenience. Mine was installed on a bulkhead above the stove just under the cabin top through which it vented. I doubt your insurance company will like the ones with a pilot light though. One possible solution would be to install it in a locker that is only vented outside the boat like a propane locker. Not the same one the propane is stored in though.
There is one with no pilot light that looks pretty good. Here's the link.Gas Water Heater
It has electronic ignition and has no pilot light. The flame when in use is just below a horizontal radiatir like panel through which the water travels. Very convenient as you dial the temp you want and no cold mixing is required at the tap.
I have never heard of a diesel powered instant water heater - doubt they exist - at least in a size for a boat.
Why would fumes and gas concentrate around the transom? And what do those swimmers do when near the exhaust of a running generator? That's not very healthy either but best not to tread water near any exhaust I guess.
The Paloma type instant gas water heaters vent through the cabin top or side right beside the unit.