Checks are processed by the Federal Reserve, not the banks! It may depend on a bank's distance from the closest federal reserve, not the distance from bank to bank.
This is really the point...
That is incorrect. The Federal Reserve processes some checks, but not all. Many banks, especially those close to one another and virtually all large banks have "direct presentments", in which they bypass the clearing agents. Also, many community banks (such as the one I work for) share regional data-centers that act as mini-clearinghouses. There are also larger regional clearinghouses that bypass the Fed. Part of the reason is that the Fed is generally the most expensive of the clearing mechanisms available.