Emperor's New Groove was the closest they did (which is why El Dorado and it are considered "cousins"). If they had gone down that route for their films, they might've had a shot in keeping to 2D.
I would actually disagree, when the film came out, many took it as Disney's conceit that they were dead as a studio. It was a film seen as below Disney, a poor attempt from a fledgling studio to be DreamWorks/Warner Bros..
A big problem for Disney was that they were the original Pixar/DreamWorks, but only for 4 films. Adults loved The Little Mermaid, Beauty and the Beast, Aladdin and the Lion King. All these films had tight scripts, incredible music, and a general sense that everyone on staff wanted these to be for adults - evidenced by the Oscar nominations. When people think Disney, it is basically these films, so something like Emperor's New Groove didn't sit right with audiences. It lacked the grandness that made the golden 4.
Tangled was the true best direction for the studio. It modernized Disney with some DreamWorks humor but ultimately gave audiences exactly what they were looking for, a new Princess romance film without any of the bullshit from late-stage Renaissance. The animal characters didn't talk, so no Rosie O'Donnell or Eddie Murphy tanking the film. Both were also written to have an edge and importance in the narrative, so they aren't cute fodder like they would be in older films. No jingling keys to keep kids' attentions, a problem that is arguably present in Hercules with its ADHD pop-culture reference style and especially present in something like Home on The Range. Tangled won by just having a tight script that housed an extremely likable romance, all with a few nice music tracks. Disney following up with Wreck-It-Ralph, a film that is basically a stealth Pixar flick really highlighted what direction the studio should have been on a decade prior. They were able to take the best of their roots, while also experimenting with more adult tales on the side. Lilo & Stitch shouldn't have been a fluke, but a type of film that would alternate with more traditional Disney to keep the studio from just being musicals.
Instead, 2000s Disney was a desperate attempt to capture a male audience at a time where Disney was guaranteed to get slaughtered doing that. They were never going to compete with the raunchy comedies of studios like DreamWorks and they were never going to compete with action flicks amongst Harry Potter, Star Wars, LOTR, Spider-Man, X-Men, and even their own series with Pirates of The Caribbean. Them being a girl studio arguably would have kept them distinct in this period, they just needed to rid themselves of the kid garbage, maybe take a queue from YA at the time.