No, the height increase is only by a factor of 12/7, which is about an extra 71%. Compensating for this, there is a width reduction caused by the loss of accide

No, the height increase is only by a factor of 12/7, which is about an extra 71%. Compensating for this, there is a width reduction caused by the loss of accidentals. There is also no need to waste space on unused octaves, so there might not be any height increase at all for some pieces of music. Trivial transposition is a highly desirable property.