This is the way to do it for modern audiences. Opening credits (with a few notable exceptions - “Spider-man 2” being the first to come to mind) are usually a snoozefest for the audience, especially considering that said modern audience already had to sit through 15+ minutes of trailers, commercials, and theater informational clips.
Creatively produced end credits can be used to “call back” to the movie the audience just watched in an entertaining manner. Sometimes this comes in the form of a blooper reel. Pixar movies frequently use the approach described above for “Captain America,” using animation to create little side stories involving the characters (“Finding Nemo,” “Ratatouille”) or even to add epilogues to the main story (“Wall-E,” “Toy Story 3”). In a few particularly inspired instances, Pixar even created animated fake blooper reels for their credits sequences.
By putting the credits at the end, modern moviemakers avoid deflating the audience’s enthusiasm before the movie even begins. By using the raw material of the movie the audience just watched to pep up the end credits, they create an incentive for people to stick around and find out who is responsible for the production. It’s a win-win situation.