If I have to do something new with the list, I don't have to completely rewrite my program (like #1 does)
You said #1 only took 15 minutes. Hardly seems like a big cost. If you never have to rewrite, #1's the right answer. Or if the rewrite includes functionality never even anticipated in your "correct solution". If it's that small, starting over with a clean slate may be faster than fitting in new functionality.
But say instead that it's a larger problem, and that #1 takes one day to build, #2 takes a week, and the "preferred" solution (call it #3) takes two days.
Then along comes your change request. It will take most of a day to rewrite #1 to do something never anticipated, but it can be slotted into #2 or #3 in about an hour.
Now you've broke even between #1 and #3, and that's only the first change request. Any real system is going to get many more.
These numbers are pulled out of thin air, of course, but they're pretty accurate according to my development experience.