BlazBlue already had a comeback mechanic, you start automatically gaining meter when low on life.
In terms of the overdrive though you need to understand it completely replaces the gold burst system. Now if you burst in a gold burst situation it takes your burst and puts you into overdrive, in essence you need to choose between an overdrive or a defensive burst. The value of a defensive burst is not really static throughout the whole round though, if you get hit without a burst at 95% health you're almost definitely coming out of that exchange alive but if you get hit without a burst at 25% life you're almost definitely coming out of that exchange dead. If the overdrive didn't scale in strength as you lost health than when a player was low on life the green burst might just be too useful for the overdrive to be worth it, this way the overdrive is always remains relevant compared to the green burst and you can decide whether you want to spend your burst defensively or offensively at any point in the match. Think of it as the overdrive scaling to match the green burst in importance.