This has been discussed before. With the global cooldown, separating biotic-tech-combat cooldowns would benefit ONLY the sentinel. Consider a Sentinel with a combat bonus power like Proximity Mine: all you do is spam Tech > biotic > combat > tech > biotic > combat... and so on.
And generally speaking, while it may not make 'sense' lore-wise, gameplay-wise it makes total sense for balancing reasons (as stated above).
And if you really want to have a lore reason, then assume that your hardsuit manages your battery power, and also replenishes your energy/fluids/whatever after unleashing your biotics. Remember the codex, lore-wise biotics can only display a few biotic displays before they get weak. After using a biotic power, the hardsuit can inject you with enough nourishment or fluids or whatever so you can continue to use biotics at regular intervals. In short, just think of the hardsuit as regulating your powers so you can continue to use powers of any type at regular intervals, instead of brief displays of awesome destructive power but nothing else for the rest of the day.