You're coming at this decades later. Part of McCoy's work, dramatically speaking, was to serve as the original viewers' stand-in, to point out how alien he was, how different. That way, we get to see Spock struggle with his human side, question himself.
And yes, of course the character was the polar opposite of Spock: emotion vs. logic, with Kirk in the middle. Yes, it was a little strident at times, but it's the same dynamic as in the cell scene in "Bread and Circuses," likely the best McCoy/Spock scene of all time -- and in the third season, at that!