When I'm ready to tackle a new piece, I always first study it away from the piano, as suggested by the Leimer/Geiseking approach, although I don't go quite so deeply into music theory. I do comb the score with a fine-tooth comb in other ways, however. First, I make a determination on the general form and structure of the work to get a macro view. Then I consider the key signature and tempo for awhile. (Anyone here who has made studied judgments on the meaning and application of "andantino", for example, which has given pause to musicians for decades, will know why this is important.) Next I try to get a sense of the character of the piece by paying close attention to dynamic and expressive markings, special directions, and tempo and key changes as well as accents. Then I carefully inspect figuration relative to types of touch employed, articulation, phrasing, voicing of chords, voice leading, foreground versus background, presence of inner lines, important harmonic notes for coloration, notes to be deemphasized, really difficult ledger lines to read, short cadenzas, unusual rhythms to be analyzed, tentative fingerings, and the most likely helpful practice methods. I even start to form preliminary ideas for pedaling.
For a lyrical piece (having accompanied singers in the past), I think about how the melodic line might be sung, and in so doing, get an initial sense for playing the long line. I'm also on alert for the melody shifting to the left hand. If I'm using an urtext edition and see something unexpected, I'll consult the editorial committe's commentary to see if there is any mention of it. I'll also pull out repertoire guides and other books to read more about the music and the composer's intent. As I'm doing all this, I mark the score as much as I need to. There are undoubtedly other things I look for than mentioned above, but you get the idea.
By the time I actually sit down at the piano to read through the piece for the first time, I already know a lot about it! That means that practicing can be more accurate and efficient from the get-go. And, I can proceed to specific problem solving more quickly too. Because my practice time is limited and precious, this approach is extremely useful to me.
Unfortunately, it's impossible to know everything about a piece by studying the score alone. It will invariably reveal some of its deepest, innermost secrets only in the playing. As I gain new insights and work on them at the keyboard, I again later take the score away from the piano to consider those further, and to make additional notations on the score as to my objectives.
Studying the score beforehand really works well for me. I have not sat down at the piano to "muddle through" the first reading of a new repertoire piece for a very long time. It's simply not effective. Rather, studying the score away from the piano accelerates learning and knowing.