Sprints are timeboxes and not deadlines. Stuff is done at a "normal" pace and it either fits (or does not) in that timebox.
Fundamentally, it does not really matter in itself. Noting down whether the estimation was correct or not, though, is important.
The whole point is that a team is supposed to get more _predictable_ over time. They learn how to estimate better, and having a fixed "box" to fill is a very easy way to do so.
So: Scrum is a "scientific" way to reach a sustainable pace ("scientific" meaning: based on objective, repeated measurements).
This is not to say that Kanban does not work. It's just way way harder to do right, because measurements of how good a team is at having a sustainable pace are not as intuitive and are easy to ignore for teams -- and ignore it they do, unless they are very well disciplined.
But all of this is well know in the world of Agile, I remember talking about this ten years ago. Perhaps an agile coach would truly help this person.