What Makes a Game a Good Toy

I recently played through Just Cause 3, and had a lot of fun playing that. - I think, though, that after ‘liberating’ all the towns, collecting all the collectibles, and completing all the missions, there’s not as much innate incentive to play the game as I would’ve thought.
Considering Just Cause 3 is a game where you can fly-like-batman, grapple, and parachute your way around an environment, in addition to blowing-shit-up, hijacking all kinds of vehicles easily, etc. etc. it’s a bit strange. – I get the impression it would be fair to describe Just Cause 3 as “a game where you unlock things, so that you get a fun toy/playground at the end of it”. (e.g., unlocking more vehicles to request, or unlocking a higher request-tokens capacity as you get nearer the end). – So what makes for an interesting ‘toy’ game?

Minecraft is the ultimate ‘toy’ game.
To such an insane extent. Google for it, but you hear of things like people building BASIC interpreters, or processors, or whatever using the redstone mechanics.
From what I’ve played, I think why it’s fun like this, more specific than “you can do anything you want (like farm, or fight)”, is Minecraft involves creating systems. (e.g. “here is my house, here is where I mine, here is the chest were I put stuff”). And so the narrative follows from that. “Here’s my mine… I’m going to mine further”, “here’s my house. I want some glass, so I’m going to get sand”, “at night, I need to fight my way back to my house, clear the surrounding area. Or maybe just survive the night through combat”. – I suppose there’s motivation which comes from taking a wild/unordered region (the generated world), and conquering/colonising it; e.g. tunnelling through the underground, chopping down trees, terraforming uneven parts of land.

Minecraft is quite, quite different from Just Cause 3, in that the latter is much more obviously a “game” than the former.

The Saints Row series is much closer to what Just Cause has. (In particular, I like Saints Row the Third best, but whatever).
Both these games involve having fun from destruction and unrealistic-violence in a conquerable, open-world setting.
I’ve certainly had a lot of fun screwing around in Saints Row the Third. – Though, unfortunately, if Saints Row is a better toy, Just Cause is a better game: the minigames (and missions) in Just Cause aren’t boring.

So what makes Saints Row a better toy?
I wonder if part of it isn’t that in Saints Row, you get the ‘cheats’ like Invulnerability, Infinite Ammunition in-game. You have to buy them, (& so there’s strong incentive to play the game to earn the money, etc.). – Free reign to cause havock and destruction, after earning this by playing the game ‘legitimately’ sounds fun.
And while you can’t construct/modify the environment, so can’t “create systems” like in Minecraft, Saints Row lets you customise your character and your character’s things. The character’s body/face/hair, the character’s clothing (& what colours), the weapons (to an extent), and the cars. – You can choose to dress your character in all-yellow, driving an all-yellow car if you want. (Why not, right?). I think your character can even have actually-yellow, also. Or you can dress up in costume. – I guess that’s very Barbie-doll ish. But it’s fun.
The setting in Saints Row does lend itself to some narrative-making: gangsters from your gang will roam the streets, as will gangsters from other teams, and the police. So you can easily pick fights if you want, & then have a good ol’ car-chase to escape. There’re also random-events like “defend this area for 3 waves” which the player can be prompted with.

Just Cause 3 has some of these things that Saints Row has: there will be random encounters / mini-quests, involving tasks like “hijack this car, then get clear of your wanted level”. And you can ‘collect’ different vehicles. You can certainly cause mayhem if you want, & there will be patrols of bad-guys you can pick fights with every now and then, too.
One (dumb) idea might be, that the enemy would try to re-conquer towns/areas that the player ‘liberated’. – This would have some narrative, but makes it quite a chore to keep the whole territory ‘liberated’. – There’s no benefit from the ‘liberated’ regions that impacts the player much; not like “more reinforcements to help you” or “hourly cash income”. (Well, the ‘main’ benefit actually seems to be there aren’t as many bad guys, and you can do ‘suspicious’ things without getting a wanted level. Still). – What I do like from Just Cause 3 is that you can always have some town/settlement “re-oppressed” so it can be “re-liberated”.
Perhaps the whole “not using cash to upgrade/unlock stuff” is strange, also.. in that, it demands skill to unlock better features (like “more ammo capacity”), rather than demanding player spend “more time playing the game”.
– And Just Cause 3 has some cool.. features that lend itself to being a fun toy, like the tether.
But I wanna be able to customise my car, to be able to tear-shit-up with infinite-rockets, & screw-around in pew-pew shootouts without worrying too much about things like ammo, or health. (Which isn’t really a “game”, sure).

All the same, I can’t help but think that a marriage of Just Cause 3 and Saints Row would be a ridiculously fun carnage-causing sandbox.