D&D 5E - is the dodge action broken?

Directly it doesn’t. But indirectly your Dex is already accounted for at the attack roll. Having 20 dex raises the difficulty for the roll (your AC) and thus makes the roll with disadvantage even more prone to failure.
For example, attack with no bonus vs for with no armor:
With dex 2, AC is 6, there is 75% hit chance normally, 56% with dodge action.
With dex 20, AC is 15, 30% hit chance normally, 9% with dodge action.

If the dodge action gave any bonus based on your dex it would effectively be accounted twice for the roll.

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