Except real life doesn't work like that.
Surprisingly Realistic Outcome occurs as soon as the fourth movie started. Bonnie, despite her initial enthusiasm for Woody, eventually grows bored of him as she finds more interesting toys to play with. Anyone who expects that toys can simply find a new owner and assume the cycle would repeat itself just as it was with the previous owner is in for a rude awakening because not all children are alike. Some children prefer some toys over the other, and toys that used to be a favorite of their previous owner might be The Unfavorite for the new owner. Woody learns this the hard way, which also has the effect of shaking the long-standing Undying Loyalty that defined him for the entire series to its core.
This goes both ways as well. Just as Bonnie doesn't see Woody the same way Andy did, Woody also can't bring himself to truly bond with Bonnie the same way he bonded with Andy, which is supported by the Freudian Slip during the talk he has with Forky when he inadvertently said Andy's name instead of Bonnie out loud, showing that even though he has a new life with Bonnie, he still can't bring himself to move on from Andy due to being his oldest toy. The other toys including Buzz managed to move on from Andy because they didn't have that special bond with Andy the same way Woody did, which is why Woody is the only toy who still didn't get his closure. Being The Unfavorite also didn't help at all.
Thus, Toy Story 4 is what happens when you presented a story that sets after the supposed Grand Finale where everything is seemingly resolved, only to find out that it really isn't the case. For Buzz, Jessie, and Andy's other toys, their stories are already over, but it's not the case for Woody, who still needs his personal closure, which is what the main crux of the movie is about. Woody's chance reunion with Bo Peep, who learned that her old life is over and she has to adapt to something new in order to live a fulfilled life, is what kickstarted Woody's own personal transition from an old cowboy who's always there for anybody who needs him and will move heaven and earth to make them happy, to someone who still actively helps others but in such a way that he himself finds personal happiness as well.
"If you want a happy ending, that depends, of course, on where you stop your story."
Except realistically you can't really do that. You can't simply just pick a moment in time where everything is at its highest point and ends your own story right there. As much as you hate it, life always goes on and things are constantly changing, and some of these changes might not be what you're used to and you may find yourself questioning your entire life so far, but that's how reality is. You have to learn how to live with those changes the best way you can until your journey truly ends. This is the crux of the lesson that Woody must learn over the course of Toy Story 4.
For a Grand Finale may have ended your story, but it isn't the end of your life.