The main reason is that the makers of TMP wanted to overlook the actors' aging, while the makers of TWOK wanted to embrace it and use it.
But Kirk also cited "my five years out there," which means his last "star hour" can't have been more than a couple of years after the end of TOS (or more than a year after the end of TAS). And Scott, Sulu, Uhura, and Chekov were only one grade higher in rank than they'd been in TOS, suggesting that not a lot of time had passed. By TWOK, not only had Sulu and Uhura jumped up one more grade to full commander, but Chekov had jumped up two grades to equal their rank, and become a first officer, a major step up in responsibility from his security-chief posting in TMP. That makes it pretty clear that there was a larger interval between TMP and TWOK than there was between the 5-year mission and TMP.
Also, we know from later canon that the 5-year mission ended in 2270 (per Voyager: "Q2") and that the TWOK-style uniforms were in use by 2278 (per our glimpse of the Bozeman in TNG: "Cause and Effect"). So we know TMP must have happened sometime between late 2272 and 2278. TWOK would be 2282 if it were 15 years after "Space Seed," but the Okudachron puts it in 2285, presumably since TFF has to be close to 20 years after "Balance of Terror" to account for Nimbus III's backstory. This date is supported by GEN, where Kirk ends his period of retirement with Antonia and goes back to Starfleet in 2284.