The city actually used the system from the 1920's through the 1950's. According to this history of PR, the end of the system in 1957 was fueled by fairly nasty, racist motives:
In Cincinnati, race was the dominant theme in the successful 1957 repeal effort. The single transferable vote had allowed African Americans to be elected for the first time, with two blacks being elected to the city council in the 1950s. The nation was also seeing the first stirrings of the Civil Rights movement and racial tensions were running high. PR opponents shrewdly decided to make race an explicit factor in their repeal campaign. They warned whites that PR was helping to increase black power in the city and asked them whether they wanted a "Negro mayor." Their appeal to white anxieties succeeded, with whites supporting repeal by a two to one margin.
In the same article (almost as an aside, despite its seeming importance), the Enquirer reports that Jeff Berding plans to ask Council to approve another Charter amendment for the November ballot. His proposal would implement the 2004 Election Reform Commission's recommendation (scroll to page 9 for the pertinent discussion) that Cincinnati move to a true "strong mayor" system of government. As noted in the linked document, under Berding's proposal, the Mayor--not the City Manager--would appoint administrative officers and department heads, like the City Solicitor, the Directors of Finance and Public Utilities, and the Superintendent of Water Works. The City Manager would be replaced by a "Chief Administrative Officer" who would serve at the pleasure of the Mayor (Council's advice and consent would not be required for appointment or removal) and have only so much power as the Mayor chose to delegate to ensure the day-to-day operations of the City. And the Mayor would no longer have a role in City Council (instead, Council would elect its own President, equivalent to the Speaker of the House in Congress, and select its own committee chairs).
Intrepid Cincinnati Blog readers will remember that we had a discussion about these issues earlier this year (here and here). If either or both of these proposals makes it to the ballot, I anticipate that we'll discuss it a lot more. But these are huge changes in the way City government would be elected and operate. If they're on the ballot, I hope we have a broad, City-wide discussion that isn't completely drowned out by the presidential and county-wide elections.