There have been Kings who have been great warriors. Richard I comes to mind. Henry VIII took his martial arts pretty seriously, if I understand correctly.
But they don't have mad levels in Fighter because of their enormous incomes.
That's because gold for XP only really makes sense for plunder. The inherent assumption in the system is that the gold in question was *guarded*, whether by traps, tricks, or monsters. It required some skill - whether in cleverly avoiding the threats, or by battle, etc. etc.
On the other hand, the income coming to a landed knight, baron, earl, count, king, etc. is due to the office, and requires no special skill, ability, or even action on the part of the earner. Similarly, if someone's father dies and leaves the 2.5 million gp, that person doesn't suddenly skyrocket 5 levels (or even one, if you're playing that you can't go up more than one level in a go). That's because they didn't do shit for it.
Windfalls, rent, investment incomes - none of these should generate XP in a gold for XP system.
Because of that, kings should be modestly levelled, if at all. An average man-at-arms or landed knight would likely have more Fighter levels than a king. (That reminds me to rant about the 0-level man-at-arms - the idea that a professional fighter doesn't have a few levels of Fighter is laughable).
At this point, some may be tempted to say, "OK, so kings aren't 20th-level Fighters, but maybe they're 20th-level Kings!". Well, let's examine that.
What class abilities would a King have? What do Kings do? Well, they drink and feast and hunt and whore, but those are well within the reach of anyone who has the wealth. Those don't need to be class abilities.
They conduct diplomacy, and manage the affairs of the kingdom. Or they appoint someone to do that for them. You could maybe argue that levels in King increase reaction rolls and increase kingdom revenues.
When you come right down to it, though, being a King is pretty much just being a normal guy, only richer. I have a pretty hard time accepting there's enough for a whole class there.
Where does that leave us?
Well, kings are just normal guys. They get power not through class levels, but through the dignity of their office and through the vast wealth and incomes that come with the title.
Gold is its own reward. Gold brings its own power.
You don't need to add personal power on top of the economic power wealth provides, unless there's some factor of personal bodily risk.