Kamisori are used with one specific side against the face at all times. That side is the unstamped "Omote." The stamped side, which has a much more pronounced concave, is the "ura" and it is to be used away from the face.
The use of Kamisori is a tradition. It is the way it is. I can't answer you as to "why" or whatever, but if you look at the blade profile of a Kamisori, it's pretty obvious that the two sides are different, and thus the use is going to fit that profile. If the use was, as you would like, symmetrical, then the blade would be symmetrical.
This isn't a recommendation or advice, this is the way that they are used, much as when you drive you don't use your right foot on the gas and left on the break. It is what it is. Yes, it's difficult. But it certainly can be learned, if you want to learn it. I have learned it, and I know several other Westerners who have done. And of course, everyone I know in Japan who shaves with one does so.
Now, as to whether or not you can do it another way, well, that's the thing about the word "can." Of course you can shave any way you want. You can use your razors to slice garlic like Paulie in Goodfellas. But in that case, then you are forcing the tool to adapt to your skills, rather than adapting your skills to using the razor the way it is designed to be used. You are ignoring the hundreds of years of tradition and use that produced these razors.
In which case, I have to ask: Why have them and use them at all if not to experience that tradition? Western style folding razors, which are naturally designed to shave the way you seem to want to shave, are cheaper, more widely available, and in many ways easier to use.
I hope this answers your questions.
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