It's quite simple, the empire was far to big for one man to rule. With increasing threats on all fronts it was simply to much for one man to be able to control it all. It's hard for one man to fight picts in Britain and at the same time give orders to men in Syria how they should handle a Persian invasion that may have incurred several weeks earlier.

Furthermore there was actually no such thing as "western" or "eastern" Roman Empire. It was one empire split into administrative halves.

When the western part of the empire collapsed Odoacer (who took control if Italy) sent the Imperial regalia to Constantinople and told Zeno (emperor 474 - 491) that one emperor of the Romans was sufficient.