The maniple would have served as a way to keep the formation when deploying and advancing, so men would know where they should be. I don't know any battle in which it could have been used as a tactical unit, and indeed would have been too small for that role. As someone stated above, you need a certain firepower (shockpower in this context) for this, plus an efficient command system down to that level.
A checkerboard seems to me absurd as a combat formation. Faced with a continuous line, the men at the extremes of each "cell" would have to fight against 2 or 3 enemies, would succumb most of the time, the "cells" would become thinner and the gaps between them wider. That formation would have been used for deployment, that is, between the column (a marching formation) and the line (a fighting formation).
I didn't see anything eccentric in Delbruck's work (maybe in his time he was). Granted, after 80 years, it is outdated (particularly the latter volumes), but as a starting point in the study of ancient warfare I know nothing better (not that I know a lot of literature on the subject, by the way).