It can only come through on your smart phone if you have cell service. There are many areas in a National Park where you may be sightseeing that don't get cell service - so you will not know the dog is barking until you head back to an area where there is cell service.
Now if you never travel and stay where cell phone service is limited, then the webcam is very helpful. And spending the majority of your time in places with service can definitely give you a better idea of whether your dog will bark a lot or not.
But not every campground has effective internet service and not every place has cell service. And not every RVer limits their travels to areas with internet and cell service.
So you need to be aware of potential gaps in the reliability of such tools before depending on them.