It really does depend on the game. As far as canon pokemon games go, I too lose motivation to do post-game stuff. A lot of that stuff is backtracking, or just doing competitive style stuff in battle-towers/trains/etc. Other times its just ludicrous things with Looker, Interpol's daftest agent.
A lot of the problem with post-game stuff that I've noticed is that it's usually very vague/open ended and leaves you to discover for yourself by randomly revisiting places you've already tread over hundreds of times before. Some of that is nice sometimes (mostly if it was hinted at early on that you can't go there until X/endgame happens, like Mewtwo and Cerulean Cave), but most of the time linear, directed main stories are nice are because they give you clear goals and destinations to shoot for, encounters to prep for... honestly, the best postgame stuff I'd have to say is stuff that continues the story from the climax that helps tie up lose ends or hints at what's coming next in the series while still providing a challenge. Parts of the stories that you want to find out how it wraps up, but aren't as big and epic as the overarching conclusion of the game's climax. Like, a decent postgame for sun/moon would have had you rooting out the last strongholds of the laughable team skull instead of completely ignoring them to hunt completely absurd and ridiculous 'ultra beasts'.
If a game is all wrapped up and finished in all its story lines and tangents, you don't need a post game. But if you wanna provide more challenges and loot that maybe didn't fit in line with the progression of the main story, or tie up the loose ends, the post-game is very important. Like, post-game for a persona game generally doesn't make sense, but it does have a new game+ if you wanna get to things that activities, time, and knowledge did not permit the first time around.
You know how some 'based on a true story' movies will have that little captioned slideshow telling how each person ended up after the events of the movie? A good post game is like that. But instead of a slideshow, it's a fulfilling experience that gives the fan closure.
For many a poke fan, post-game content is actually a nuzlocke run. Something to continue the challenge and growth of skills and tactics of the main game. Just keep in mind that most games reward challenge achievers with some kind of mark/emblem/distinctive gear that lets other people see at a glance that they were able to overcome certain challenges and requirements. Games like destiny grant you exotic or exotic looking gear and weapons, while games like megaman give you a collection of stars at the start screen to tally up your biggest feat completions.
Post game is always optional, but many gamers like it more when there is a reason to come back and play a game even after the main story is over.
I've a question for you Ame. Imagine you are done with the game, the main story all told and over with. What would be DLC content to you, thinking of it like a commercial game developer? Would you make story segments, reliving the moments that brings to life the backstories of certain reborn characters that were only revealed in exposition in the main game? Playing as them, experiencing the world as them as they live and narrate their lives until they come across that point of no return where they fully become that person that the player meets and interacts with in the main game? What are the possibilities that you see, Ame?