You couldn’t make Toy Story today because NOBODY should be okay with how disturbing Sid’s face is.
On a side note, with all the remakes that are made nowadays, why has there not been a shot-for-shot remake of Toy Story using Pixar’s modern tech? Please, fix those terrifying lips. PLEASE
You no longer need to use 10 step chains of parenting and unparenting to cobble together an animatable model, those data files are about as useful as a automatic loom's punch card system. They were badly stitched together in the bad old days. The only way to do that would be to make the film from scratch, and I can't imagine anyone would want to do it.