Do potatoes cook faster boiling

Yes because the temperature it hotter in the stove than in water. It takes longer for water to boil then a potatoe to cook. And baked taste better.

(2) I have a different view. Baked potatoes are usually cooked whole or in large chunks and in order to be baked they must be cooked in the oven - it takes time and energy to bring an oven up to the right temperature and you have to heat the whole volume of the oven to do so - that is not cost effective.

It takes less time to bring a pot of water to the boil to boil potatoes especially if you start with hot water from the tap - you only need to raise the temperature a few degrees. And you are only heating the volume that will actually be used for cooking, not the whole oven. Furthermore, potatoes, especially if they are going to be mashed or used for potato salad, can be cut into small pieces beforehand, this further reduces the boiling time.

As a rough rule of thumb I would say that a potato that took 45 minutes to bake whole would only take about 10 minutes to boil if peeled and cut into quarters first.