good points, but u have to consider where that real food is going. the tyrells and lannisters are not giving it away. the problem was that there wasnt even any food to sell. now they can continue to restock the markets, but the poor will only get scraps and slop from anybody. but what they get from the sparrows is also spiritual nourishment. it isnt only the poor joining them either, look at lancel. lancel is kevan lannister's heir and a knight and he has forsaken all his claims to land and riches to fight for the faith. he is not the only knight to do that even tho the show hasnt done a good job of illustrating that.
people back then were very religious in general(think back to davos' dialogue about stannis forsaking the 7 and burning those statues). maybe they didnt go to church all the time or at all, but if suddenly u have a bunch of armed christian rebels in your town that were legitimized by the queen herself, u gonna remember your "our fathers" real quick. u also might join them if u dont want to get run over by that train.
the answer to the riddle is yea, power resides where people believe. but its an illusion as well. right now, the faith inside of kings landing is growing and growing. cersei fukked up big time by legitimizing them and not nipping it in the bud. in no time, their power will grow beyond anything they can control considering the fact that tywin is dead. its gonna be interesting in kings landing.