A couple possibilities I see:
-- The damage and destruction from WWIII was so severe that much of our civilization and technology got knocked back almost to a pre-industrial level, and had to essentially start over from the beginning. Obviously there were still some great advances in warp and transporter technology, but by the 23rd century our basic computer
technology had only gotten back up to a 20th century level (with styling from the 1960s, of course). Either because of lack of resources or because the previous knowledge had been lost.
-- Or alternatively, by the 23rd century technology had become SO advanced and impersonal and automated (with Minority Report-style interfaces everywhere, computer chips in people's skulls, and robots doing all the work) that there was ultimately a societal backlash against it, which resulted in the return to a simpler and more analog technology by the time of TOS.
Of course the catch there is we never hear anyone reference such an event in any of the Treks. But hey, it's the best I got.