LOL - "supposed to have" ?? Good one! If we were supposed to not have them, there would have been some proscription in the Constitution. There is none. In fact, the reason Senate elections are staggered, not all occurring at once, is because experience is desired, and designed to be maintained in the Capitol. Our federal government is conservative by design, favoring experience and continuity over the lack thereof.
In national office holders, we've had Senators as young as 30, and Congressmen as young as 22. Either position can provide a wealth of legislative experience. And the voters in our democracy have always favored incumbents. Government experience matters. Go figure.
As for Executive office holders, there have been dozens of mayors in their 20s and early 30s in cities ranging from Cleveland to Ogden to Des Plaines to Pittsburgh. In other words, plenty of government experience available in the Executive branch too, before aspiring to the Oval Office at age 36.