Well, I imagine he wanted a legitimate child to be the third head of the dragon, but I’m of the opinion that Rhaegar reached back to Targaryen polygamy because it fits his whole scheme of trying to recreate Aegon the Conqueror as a solution to the prophecy of the Prince Who Was Promised.
The fact that that scheme wouldn’t make much sense isn’t actually an argument against it, because in OTL him running off with Lyanna was the catalyst for war, so it never made much sense.