This has been promoted by southern utilities for two decades. It seems like a good idea; why not? A water heater uses gas just like a boiler and heats water like a boiler. It seems that the people who make water heaters would tell people to stop using more expensive boilers and just use water heaters.
But boiler manufacturers insist that even though they do a similar job, they just aren't the same. For safety reasons the American Society of Mechanical Engineers insists that for a boiler to be used in someone's home, the metal should be about 1/4-inch thick and the boiler should use a 30-pound relief valve. Also the gas valve on a boiler should use a redundant valve - that is have not one but two valves to close off the gas in case one should fail open. There isn't that much difference between 130F water in a water heater and 180F+ water in a boiler.
It might just be that the engineers are afraid for the occupants of a home or might worry about children. For those tried and true heros who don't worry about family, a water heater with less than a 1/8-inch wall thickness, a 150-pound relief valve and a single gas valve is enough. After all water heaters don't blow up that often.
There is a slight difference, though. You see, water heaters cycle about twice per day to make hot water for showers etc. A boiler runs every hour, so it is in use 12 times or so each day more than a water heater. There is much more strain on an appliance that works every hour instead of just twice. It also usually puts out 120-140F water, not 180F+ water, so you have to use twice as much radiation as with a boiler to get as much heat into the house.
I would at least put the minimum safety accessories on the water heater so I would feel safer. I would add a 30 psig relief valve on a tee next to the existing T&P relief valve, a redundant gas valve, and a boiler high limit/circulator control. These added items make the water heater as expensive as a boiler. I don't know if I would still feel safe with that little metal between me and oblivion. Some municipalities forbid using water heaters that are not rated for boiler use; so insurance will not pay for violations of local code.
I know a water heater is warranteed for 10 years if I get a quality one, whereas a boiler heat exchanger warrantee is good for 20 years. I don't know of many water heaters lasting 20 years, most last 7, so you can install three water heaters over the 20 years. But if you move often, the next guy can get stuck with the replacement. You might save $200 by doing this if you move out within 6 years. This amount could buy the family two good dinners.
I definitely would not use the same water heater for heat as it makes hot water for washing. When the radiation is unused in the summer time, the water sites there over the season and can help grow legionella. Legionnaire's disease kills the unfirm by attacking the breathing.
I wouldn't worry about a leak in a sealed hot water system that has no fresh water entering the system where it could leak a gallon or two. I would however, worry about a paper-thin baseboard tube bursting to spray as much city water around my house at 40 to 60 psig with an unending supply of water until I got home.
But each generation reinvents the wheel trying to find a way to beat the cost by doing innovative things like using a water heater instead of a boiler. Like unvented heaters are rediscovered all the time; breathing the products of combustion seems feasable, they make them don't they?