5e doesn't have a take 20 rule because the whole endeavour was uninteresting to start with.
I suppose how interesting something is varies from person to person.
That is because 5e is written narrative first while 3e is written simulation first.
Uh, it wasn't really a simulation at all. In fact there are lots of things in 3rd that didn't reflect real-life at all. Certainly was more crunchy, though. Every RPG I've ever played was Narrative first, regardless of the mechanics that support it.
In any case, I used take 20 to determine whether something was possible at all:
- was it within your skill-set? Given a 20, can you succeed
I used take 20 to determine how long an activity will take, given unlimited time:
- A roll done as 1 action, one minute, one hour.
Determine whether there will be an interesting outcome to a roll:
Using that framework, you Narrate the results.
If the DM decides that a PC can succeed at something and it won't add to the game, you just narrate the result. "How long do you spend on it? This is what happens."
If there's actually a consequence for failure or if time would be a factor, taking 20 could actually lead to interesting results because the players are saying: "I choose to fail over and over again, regardless of the consequences AND I am ok with it taking a very long time, regardless of the consequences of taking that time."
Then you narrate it the consequences of their actions. The consequences should be interesting, otherwise, why call for a roll in the first place?
If there's no consequences, there's no need to roll and therefore, no need to use any specific rules. That's like the training montage in a movie. You just hand-waive it and time passes and now the Karate Kid knows how to do the Crane Stance.
In most situations, in the games I was in or running, taking twenty wasn't done lightly. There's an argument to be said that taking 10 is much more boring.
The story-telling between 3e and 5e hasn't changed. Only the the mechanics that lead you to the results.