Forty-five years ago, Ford brought us some mighty hardy manual transmissions. The Top Loader three- and four-speed transmissions were tough and durable, and they remain the standard today in all-out competition because they don't break.
But what were Ford engineers thinking when they designed Mustang floor shifters? They were terrible right off the assembly line and only got worse with time and use. We'd have to ask the same question of Chrysler engineers, who came up with the same broomstick-in-a-barrel floor-shifter for Plymouth and Dodge performance cars before switching to the Hurst units in its muscle cars. Ford did the same thing in its muscle cars starting in 1970.
If you're not inclined to install an aftermarket shifter, there is hope for factory shifters by rebuilding with a Scott Drake Enterprises Shift Repair Kit from Virginia Classic Mustang. Three- and four-speed shifters are basically the same except for reverse lockout on four-speeds.