in Lain's Frederick game, he waited until researching steel to slow-build start forges and barracks while running Caste and OR to make great merchants. then he switched to Slavery to whip some forges, and (because of trading issues) later switch to Theocracy to whip a catapult and a trebuchet in every city - all in about the span of 8 turns. [he also whipped the units, but didn't l et them finish until steel was ready]. he used 2 great merchants to upgrade them to level 2 cannons en-masse.
seems like the forge was useful for whipping those units rapidly - he had so-so land, so the forge made whipping units more efficient, which he needed because regrowth wasn't going to be that fast. he also wanted to get to grenadiers, so he didn't want to kill his tech rate by building units gradually or whipping away too many good tiles.
so that's i guess an instance of deferring the forge and barracks to instead pour it into beakers via building research and scientists, so that you can get a breakout unit (cannons) early, and then really launch your army fast because you have all that population stored up to turn into units.