I'm just wondering how the thought that Eirika might not have children has never crossed anybody´s mind.

I've thought about it. I made Eirika childless in one of my stories (though Ephraim married L'Arachel and had a child in that one). But two of Eirika's endings mention children (the Saleh one and the Tana one), and none of her brother's do, so it's more likely that she's the one to continue the line, IMO. We know that she can, anyway.