To look at this from China's perspective (one of the many possible), must understand that China practises tight foreign exchange controls, and with individual bank account owners the only real implementation of those controls is to limit the amount of money that each individual can exchange and transfer in a time period.
If every tourist or random business visitor could open a bank account, then it would open a hole possible to abuse and risk the stability of this system.
In similar vein, I have registered a business here in Kunming that is supposed to get revenue from abroad by exporting services.
But that revenue is delayed because (due to our company type) we don't have capital investment in cash, and in place forex authorities demand a bank deposit equal to how much foreign currency we want to import per month.
Basically the authorities want a deposit before we can bring in money to the country, which sounds a little weird - but understandable knowing TIC.
Also TIC - recommendation from the clerk at said authority was to have our foreign customers make payments to our personal bank accounts in China, because that's what everyone does.
And there again is a reason why other authorities may want to limit bank account openings for foreigners without residence permits.