I don't claim to know all the inner workings, but my educated guess for why this is impossible is that, for one, the companies that own these consoles (Microsoft and Sony) have to OK everything that is downloadable on their consoles, so that no harmful or illegal content is going through and getting them into trouble.
Therefore, every single piece of CC would have to be checked over and go through an approval process before becoming available, and with the amount of CC on the metaphorical market for Sims 4, this would never be even remotely feasible. MS and Sony don't want to be responsible for any of that, and they wouldn't allow unvetted content on their consoles that can create game-breaking bugs, glitches, crashing, etc.
Secondly, the Sims Team doesn't want to be on the hook for that either.
That's why, with mods on PC, they make it very clear that they are not official content and that any issues you introduce to your game by using mods are your responsibility.
By adding them to the gallery, they would be officially integrating mods into the game they're distributing, therefore taking responsibility for any problems they may create by being poorly made or made with malicious intent. Don't even get me started on all the mods that implement illegal and explicit content into the game, which I'm sure EA doesn't want to be in anyway officially associated with.
It could also turn into a copyright licensing nightmare, where creators would either have to sign away all rights to their work or EA could open themselves up to lawsuits.
The long and short of it is that I don't think this is ever going to happen - the closest we're going to get is when Maxis partners with CC creators to make official assets for the packs and free updates, which they've done a few times in the past.