Fun topic!
A lot of larger plushies do have skeletons, but not ones that allow for such movement, as far as I know. Few different types of things come to mind!
Once you hit a certain threshold of size, fabric and stuffing kind of collapse upon themselves and have trouble creating natural support. One of my favorite examples of a "skeleton" is from Nazegoreng, who used to have a journal stepping through her process of assemblage...inside the plush is a static PVC pipe skeleton for support. Super cool, but doesn't really get the motion you're speaking about.
Aside from wire (which you hit right on the head with material fatigue), a mix of the idea of Ball-Jointed Dolls and teddy bears could create a fairly functional skeleton. A well stuffed plush is fairly strong, and could be a "bone" - the only issue you'd have is with joints. Using the concept of ball and socket joints from BJDs (although, I've not seen a ball and socket joint meant for that use..not entirely sure how you'd implement it!) and cotter pin joints from teddy bears (spinny joints, easy to use) you could create a fairly functional skeleton.
Only huge issue I see presenting itself is the lack of stretch surrounding ball and socket joints...like if you've ever had a look at knees and elbows, all that flappy skin allows for the bend...and flappy plushie skin might look worse than knees.