The problem with Chrom x Sumia was that if that is supposed to be the canon pairing, then why bother even giving Chrom more romance options? Chrom should have been locked to Sumia & fRobin only. I know many fans who support Chrom X Olivia, but even that gets thrown out the window by Fates when Laslow doesn't acknowledge Lucina as his sibling and starts flirting with her.
My guess is that Chrom was always designed to be with Sumia (as a nod to Marth x Caeda), but someone in the staff was worried about players who would want to ship themselves with Sumia or Chrom. Thus, it was removed late into the game and even the FMV was left unchanged.