Any character can fit into a 3x5 card. My level 14 cleric fits into a 3x5 card. That's a meaningless measurement. As to the complexity, that's another matter entirely, which I'll address below.
One of the things that detractors of the champion fail to realize is that they really do have a variety of options to choose between, because different weapons have different ranges and different attack parameters which need to be taken into consideration, and movement relative to enemies and allies is often even more important than that. It may all fall under the Attack action, just as the bulk of a wizard's actions are to Cast a Spell, but that doesn't mean there's a simple default. And all of that's before you take Action Surge into consideration.
To contrast, a hobgoblin has a longsword and shield, and a longbow. Given the action economy surrounding shields, it's highly unlikely to be switching between the two. It is significantly less complex than the champion is.
The most important metric for complexity, which you have overlooked entirely, is resource management. D&D is a resource management game, after all. Both the champion and the warrior have limited-use abilities that refresh both with short rests and with long rests. That's more resource management than any dragon has.
You also fail to account for fiddly little bonuses that need to be remembered, in case they come up. Warriors have advantage on Dexterity saves and initiative checks. Champions add half of their proficiency bonus to untrained physical checks, and increase their running long jump distance by up to five feet. It doesn't add much to the game, mechanically or in terms of changing your round-to-round choices, but it adds an extra degree of mental overhead to having the character in play; and while it might be worth it for the champion, which has an entire player devoted to tracking it, it's just one more thing for the DM to track for every warrior. (Although, at least it's Dexterity saves, and not "Wisdom saves against fear effects" like it would be if this was Pathfinder; Dexterity saves might actually be common enough for that to matter, once or twice.)