If the outer suburbs manage all the services you mention
  with an even lower density then of course the inner ring
  suburbs could do the same

To take East Cleveland as an example. Population in 2010 was 17,843. In 2000 the median household income was $20,542.

Nearby South Euclid has a population of 22,295. In 2010 the median household income was $59,423.

And due to progressive taxation, South Euclid's relative tax revenue is probably even higher than those household income figures imply.