It makes sense. We don't know all of it, but the desire to have Taringail as co-ruler of Andor almost certainly played a huge part in his marrying into Trakand. As, probably, did the need to keep peace between Andor and Cairhein.

Sure, Taringail could have insisted Morghase marry into Damodred, since he was at that point in a more politically stable situation. But what's the point of that? At that point, Taringail had good reason to believe Galad could take the throne in the future when Laman died. He probably felt making a play for Andor's throne was a better option to increase his net power.

We're going in circles because you continue to insist you're right without providing one damn quote! And you confuse the issues with Taringail's succession with Galad's. The actual answer is exceedingly simple.