West Bromwich is not a part of Birmingham in the same way that Rovrum is not part of Sheffield. Brum has 2 teams, City and Villa, and considering the population is twice that of Sheffield, their aggregated attendance is indeed quite poor. Same as Leeds being the same size as Sheffield, but only having 1 club. Leeds sell out at the moment, but so would Utd and Wednesday in their position. So it is true that both Birmingham and Leeds don't have the same interest in footy as Sheffield does. Which makes it all the worse in the fact that those 2 cities have teams who do actually win something now and again. Whereas Sheffield? Not so much. Since I started watching in 1966, there is a total of 1 League Cup between both Sheffield sides. (And even that wasn't won by us.) In that time, Leeds and Villa have won the league 4 times between 'em, Leeds have won a couple of European trophies, and Villa have actually won the European Cup (now the Champions League). I think they also have a two or three FA cups between them in that time, and have countless top 4 finishes. Even Birmingham City have won the League Cup. Whereas Sheffield? Not so much......
Mind you, in terms of attendances, we are miles behind Liverpool/Everton (similar size city), Newcastle/Sunderland (joint population = Sheffield), and Man Utd/City.
So in terms of interest in footy, we do OK against some cities, but shite against others. And we never, ever, ever, ever win anything..........