It's for Retina displays and higher density devices. And you need to have a higher resolution for these and since it's easier to shrink an image than resize it bigger when the files are created bigger from the start.
The files that are rasterized and prepared for Retina are usually ending with the @2x.jpg for example, because the script calling them identifies them this way. There will be a version non Retina (eg. mypict.jpg) and in the same image folder one for retina (eg. email@example.com). Some prefer to use the @2x and resize in their code instead.
The @2x is usually 2x the size of the original picture. That's why you find these templates way too big.
And yes, most people prefer to simply work on one single file for their layout and resize it instead of working on 2 different files. The @2x will certainly become a standard (EDIT eg. Higher resolution files will become a standard.)
Technically it shouldn't change the quality if the main file is higher resolution, in fact you only get benefits from this besides (maybe) the computer's performance. It's also quite practical if the elements of design are bigger; they can easily be used again for other banners requiring the same montage... even small print projects! Retina and web projects at high resolution use the same workflow as if you prepare print projects; ideally you start with the biggest size project and can then save time using the same files but smaller. This way you don't need to do the same layout 2-3-4 times!
It just makes sense to create any design at higher resolution anyway, high density or not.
"Size" is often confusing, there's the pixel units and there's the other values that can be used.
When the people you work with asked you to create a high resolution 360ppi, they obviously prefer you to keep the same size and increase the resolution! This way it also increases the pixel size.
Same picture, same "size", different resolution:
The high resolution one, more pixels.
The low resolution one, less pixels.
If it's easier for you to calculate the number of pixels and multiply the total by 2-3-4 to get the right dimension, that's alright.
Some people like to start their canvas at the normal 72dpi and then simply resample it to 360dpi (for example) before they start their work.