I have to say monk. People forget that a level 20 monk has proficiency in all saves and get to reroll them in the off-chance they fail the first time. The invisibility keeps spellcasters from targeting you while also resisting most damage options if they end up landing. They also get evasion, which makes them even better against spellcasters.
Great points!
This is all going to depend on the factors that start the combat. For example, the OP stated no magic items. That immediately disadvantages all non-spellcasters, who tend to be able to leverage magic items (magic armor, magic weapons, etc.).
But the issue is that there tends to be too much variation at the higher levels. There are three things that I think many people are discounting:
A. "Standard" build. For example, initiative is probably going to matter a great deal. So are we going to assume that this is a relatively standard class build- which is to say, a Monk will have a 20 dexterity, and a Wizard probably won't?
B. Feats. No feats? Some feats?
C. Race. While it might not matter that much, at the margins (flight?) it certainly might.
Then you get into the same two issues that I see that will always plague these debates:
1. Any debate will get bogged down into issues of preparation. Classes that can prep the battlefield, or have time to get spells, buffs, etc. in place before the combat starts are different than classes that don't need it. Call this the "Wizard Issue."
2. The "specialist" issue. I can almost guarantee that if someone comes up with a specific build that they announce (A), someone else can come up with another, specialized build (B) that can defeat A, but that B will lost to yet another build (C), while C would lost to A, and so on. I doubt that there would be one, single build that can always and forevermore beat all other builds in all situations.
That said, great reminder on the Monk being a possibility. I think people sleep on how insanely powered the Monk is at high levels ... because no one plays a high level monk!
Now, if the OP said that the combatants would be transported, naked, to the arena, it would be the Monk in a landslide.