Nixon had to run for something in 1962 to re-establish himself in California politics and be a plausible presidential candidate in 1964 in case JFK should prove vulnerable. And he wasn't going to challenge Thomas Kuchel, who, even if he was too liberal a Republican for Nixon's taste, was still popular. (Kuchel easily defeated two right-wing opponents in the GOP primary--one was Howard Jarvis--and won the general election easily.)
To ask Nixon in 1961-2 to wait until 1968 ignores that six or seven years is a very long time in politics. All sorts of things can happen that can derail one's hoped-for future candidacy.