One arguable example is Back to the Future. They started filming that movie with a completely different lead in Eric Stoltz. It just wasn't working. Michael J. Fox was who they wanted, and he basically was brought in to replace Stoltz after filming had already started. From the original DVD releases, they basically started filming the first Back to the Future with Fox in January 1985. However, once the studio realized they had a potential winner on their hands and wanted to see if they could get it ready in time for a summer release, Bob Gale and Zemeckis told the Universal brass, write some checks and they could get things done quicker. They got it done in time for the summer release and the rest is history.
Another is the first X-Men movie, for better or worse. The problems of the first film are well documented. Singer just managed to really hit a goldmine with Hugh Jackman as Wolverine and basically made him the center of the film, and audiences really took to that. But you can watch the documentary for the original X-Men DVD release, and you can see the crew going bonkers when they got handed their release date of July 2000 from Fox. Because they started filming in like mid-1999. Ian McKellan basically went straight to Lord of the Rings once he was done with X-Men.
So yeah, it's RARE, but there are exceptions to the rule. I just think in the case of Inhumans, it didn't help the production with the talent involved.