Talking completely off the cuff, I would say that Baker definitely has a strong effect on the speed of any strategy, for two reasons - the first is the opening coin token, which as pointed out means you can buy your key cards faster; the second is the delayable-Treasury, which helps smooth out unevenness of coin. It probably has the most effect in early game, where you haven't got your economy up to full power yet, and late game, where greening can cause your key cards to miss each other more (unless you've got a mega-turn strategy so you only green on the last turn); it will also help many engines mid-game, with the exception of draw-your-deck ones that are able to make full use of the deck's economy.