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Ah but there's the rub. If I'm already predetermining the outcome when I set the DC for "take 20 situations" then why bother with the setting a DC at all? Why not just narrate it away. In what way is it significant how impossible the impossible to pick lock was? In what way does it improve the story to know how easy the easily picked lock was?
I firmly believe that the role of mechanics is to arbitrate situations with variable outcomes. Whether an attack hits or misses has a variable outcome, how much damage you take when you fall into a pit has a variable outcome, if you're setting a DC for a skill check (thereby involving mechanics) that should mean the skill check has a variable outcome. That just isn't the case when taking 20, since as we've already seen taking 20 implies a predetermined outcome with zero variability.
This means that taking 20 has no significant impact on the rules or the story, the result is predetermined, not at all variable, and therefore requires no mechanics.