In your traditional system, if you want to play something a step up, you have to actually think about it; which notes will now become sharps, which won't, etc.
In my system (A though L, or more simply, 1 through 12), you simply add 2 to each note. It's easier to work about and isn't as rigidly defined by the culture it came from.
You just described https://en.wikipedia.org/wiki/Whole-tone_scale. Nothing stopping anyone from writing and playing music in such a scale, but it won't help you with nearly all the music you are likely to be familiar with.
In my system (A though L, or more simply, 1 through 12), you simply add 2 to each note. It's easier to work about and isn't as rigidly defined by the culture it came from.