I don't see much evidence that people want less theming in their theme parks, though. If anything, we have a bit of an arms race between Disney and Universal on that front that (unfortunately, IMO) has taken the Harry Potter lands as the model for trying to create lands that wholly immerse visitors in particular worlds and stories.
As far as Disney is concerned, I think the problem is that they've become too literal in imagining 'story' means a cohesive narrative which involves, for example, typing out a biography for a store owner or character on a ride rather than creating a loose backstory that allows guests to fill in the blanks themselves. Attractions like Haunted Mansion or Big Thunder are good examples of where story drives a strong theme without being a straitjacket.
Splash was a bit of an anomaly in that it did have a narrative storyline, but worked as a fun thrill ride whether you knew it or not. That will hopefully also be the case for Tiana. However, the way they have drip fed information is a little as if Big Thunder had been presented to the public through a great deal of exposition over several years about the owner of the mine, labor conditions for the miners, how fluctuating prices on global markets for precious metals affected the fortunes of those working there, and how the effects of environmental degradation would be reflected in the landscape of the mountain.