Yamauchi did extend an olive branch to Square in the mid 00s by investing money in a Square shell corporation, Game Designer Studio, which got FF Crystal Chronicles released on the Gamecube, published by Nintendo. Pretty sure the Square Enix merger helped too. Nintendo always had a better relationship with Enix than Square. Even now, Nintendo tends to favor Dragon Quest over Final Fantasy.
Square, meanwhile, built the PS1 and then collapsed under its own weight in a few short years, especially after their disastrous foray into movie-making. :(
Which they never gave up on. Advent Children and Kingsglaive. Sakaguchi was gone soon after and FF has not reached those heights again in quality. Tho I liked 12. 13 sucked. XV is blah. Kinda funny Tak and Guchi leave Square and IMO since made better RPGs than any FF game since that time. Lost Odyssey. The Last Story. Xenoblade. Then again Taks vision of Final Fantasy VII eventually got spun into its own IP. Xenogears which is easily one of the best RPGs on PS1.