Apparently, coins are spent to perform Power-Up Fusions, and I was told that that is their only purpose. Is this true?
Usually, that is all that you can use coins for. However, it is currently possible to use coins to open special dungeons for an hour at a time. Go to the Shop tab to do this. (This appears to be a limited-time opportunity)
While the coin cost to open a dungeon is high, it's not that hard to get to with a high-level team. You get about 800K for finishing a run of the Legend-difficulty weekend dungeon.