It seems like there would be more assassinations between co-consuls who disagreed on major things. Then they could just name somebody with similar ideas, or somebody who would just do whatever they said.
But the co-consulship deal seemed to work out for everybody. Why?
Cincinnatus had only one consulship. He was elected as consul suffectus (which was the way consuls were replaced) in 460 replacing Publius Valerius Poplicola who died in office and his co-consul was Gaius Claudius Inregillensis Sabinus the other normally elected consul of the year, who therefore preceded him in the office.
Are you refering to the dictatorships of Cincinnatus? That's a wholly different office and while it's true that the dictator usually appointed the magister equitum (his first officer if if you want to call it that) freely (unless the senate had already explicitly named one), that office was not meant as a check for the power of the dictator. A dictator had (in the cause for which he was appointed) quasi absolute power for the duration of the office and the magister equitum was his subordinate.