Well, of course you could write a story and at the end decide how it would make sense. And then go back to write it again, so it does make sense. I'm just thinking it would be more economical to make a concept of what happens and who is the murderer and that, right from the start.
In Christie's stories (and those alike), there are no suspects - aside of knowing that someone must have done it - until the detective reveals what happened. That is the trick in it all, I guess. You (the reader) know it must be one of the persons who are in the story - but from whats happening you can't see how anybody could have done it, or why. Usually they even all have rock solid alibis. But at the end you see that the explaination was in the story right from the beginning. And just about everything that happened has got some meaning towards the conclusion. A perfect example is "Evil Under the Sun": you see everything as it happens right at the beginning, and still don't know what it means.
So when writing you either can make a plan how this is going to pan out before you start - or you keep changing things around until it fits. Which may be quiet time consuming to do, without making mistakes.
Thinking back on this subject, I am surprised how many books and series really have used the Christie pattern. And I'm not even sure she was the first - don't Conan-Doyle's Sherlock Holmes stories work in a similar way? Although they are more working with scientific evidence that the reader does not see at first.
But other franchises are pretty much exactly using the Christie style. The series "Murder She Wrote" for example. Did you know that it was one of the most successful series in US TV? Despite having this somewhat oldfashioned look.
And even up to this day this Christie method is popular. The Brits like it in particular.
A more modern version is "Death in Paradise", a series about a English police inspector who gets posted to some little caribean island. That is pretty much exactly like a Hercule Poirot story - only with beautiful girls, beaches and palm trees and so on. At the end they usually all gather at a swimming pool, or a terrace of a tropical restaurant, to hear who did it. Also the murderer of course. :) I mean, he could have long left the island to be on the safe side - but then it would be no fun, right?
In Germany we don't have series like that. Here it's always based on a few suspects, who are pretty much obvious from the beginning. And one of them is the murderer at the end. Not very innovative, really.