Not necessarily. My 1200 works fine (I don't know exactly how old it is since it is from a 'zero' year so could be 1990 or 2000) but the previous one I had was either 1980 or 1990 and that was also fine.
Although it is widely claimed that capacitors always degrade it's by no means universal. If the deck spins at the correct speed then there's no problem to solve.

