The modern piano is asymmetrical. Make it symmetrical, you make learning scales and playing patterns easier. You shorten the length of the keyboard and increase the amount of keys you can reach by 2. Pic Related. 
As someone who plays a bit of piano, I find that interesting. But I wonder about a few things: the current layout makes it dead easy to play using the Do scale, and it gets more and more awkward as you add sharps or flats to change the key; but you tend to play much more frequently things in Do major, Fa major, Sol major... Wouldn't that layout make it that much more akward to play basic stuff?
Do-Mi-Sol would require you to put one finger in the top row, at a different distance than the one between the Do and the Mi... I don't know, it seems a bit strange to me, but then again, that was the idea of that post. I'd love to try out such a layout some day.
Perhaps if you take a slightly different perspective. I'm gonna use 12 tone to describe it, since I don't know any music theory. do-mi-sol is 1-5-8. to transpose it, you add one 2-6-9. And so forth. That is why you are not discriminating much between white keys and black keys in your memory. Instead, you memorize simple patterns. Only six patterns to memorize all of the major and minor scales--not counting one additional memory factoid to distinguish how major and minor differ (+6) Does that make sense?