dnd 5e – Do skill scores force a character to act a certain way?

This question already has an answer here:

As a group, most of the players at our table are fans of shooting statistics. This leads and has led to several surprising characters and some … a little less surprising.

Something that is quite consistent is that players are often good at emphasizing what their characters specialize according to their statistics (for example: the charismatic bard, the agile rogue, the strong barbarian). What is left behind in this concept are often the defects of the characters that come from their inferior abilities.

The roll of the dice gives us a basic way to handle this, because the character will simply fail in many of the controls related to this ability, but this only goes so far.

An example was our recent very charismatic witch (17) who was not so blessed when it came to Intelligence (7). The problem here is that the player behind the character is far from being foolish and has a deep knowledge of the history of the world in which he is playing.

The question is double:

  1. Should a DM impose a basic level of adherence to a character's stats when they are playing RP?
  2. If so, what would be a good way to enforce this?

Shouting "Your character does not know that, they are not smart enough!" every time the player makes a deep observation about the story or the use of Arcana it is very likely to become obsolete very quickly.