The problem is that the bureaucrat expands your deck and it becomes less likely that your village starts in hand with the council room. You can add more villages but this makes it more likely that you'll draw the villages without an action to use them too. The strength comes from the bureaucrat filling the deck with silver and the council room drawing the silver for good effect. They're a combo that you don't need to draw together.
According to a quick simulator test, bureaucrat + council room is fairly strong but gets worse with every village you buy. The optimum number of villages appears to be zero. It is a better combination unsurprisingly than bureaucrat + labs, bureaucrat + smithy, just bureaucrats, and just council rooms. It seems worse than bureaucrat + rabble and bureaucrat + wharf. Those decks get stronger with an extra rabble or more wharves.
