Gameplay elements and story are two completely different aspects of a product. The story of FE13 is drastically different from FE4, even for Fire Emblem standards.
It is night and day. At best it brought back the hereditary system, but the implementation and its relevance to the plot is complete different. The children, with the exception of Lucina, do not function as a plot direction or replacement. They are entirely supplementary and voluntary; the average player won't even see all of the kids on the first playthrough.
FE4, on the other hand, is literally called the Genealogy of the Holy War for a reason. Heritage was a CORE gameplay element. You don't have a choice. The game goes out with the old, in with the new. Sigurd and his company is swept under a rug, and you get some replacements whether you like them or not.
And even if you wanted to bring in gameplay elements, FE13 is drastically different from the rest of the series. The pair up system is one change that changes EVERYTHING. You can deliberately try hard enough to never let your units come within a cell of each other, but there is no denying that the game is DESIGNED for it. It begins and it ends with the dual support system. It took what FE4 began long ago, and uses it in a way that nothing else has even come close to doing.
Not to mention the game has completely different progression (IE open world, grinding, optional chapters, etc.), the outrealm and everything that comes with it, class change and branching, and modernized calculations.