Ah, you just hit on one of my most passionate argument subjects. Prepare for incoming wall of text.
When Walt Disney started his company, it was far from the mass-media conglomerate it is now, it was a two-room studio where his wife washed rostrum plates in between frames to save money. The Disney princess line-up features princesses whose films were made in 1937, 1950 and 1959.
Snow White, for example, is the very definition of 'Fair for its Day.' It was extremely pioneering for its time, and made by a skeleton crew not to appeal to little girls and sell toys, but to be screened to everyone as a feature film. It was based on a centuries old folk tale (chosen because it's in the public domain and no royalties need to be paid) and because animating realistic figures was difficult, most of the film is made up of the dwarves doing cartoony things because they're just easier to draw.
Cinderella is a similar story, Disney had lost a lot of money with Fantasia and was looking to make it back with a family-friendly, accessible tale that wouldn't put strain on the studio. Roughly half of the film is slapstick with the mice because again, that's easier and cheaper to animate.
To judge the early princesses by today's standards is like judging Gone With The Wind on its marginalized negro characters and Metropolis on its special effects; it's just not fair. Heavy market-influenced tailoring to sell the films to specific demographics didn't start happening until the late seventies, early eighties, and Disney did try to make its princesses more progressive. That said, it is difficult to write compelling female characters when your studio is hiring a mostly male crew to storyboard, and very few females were working in animation back then.
Princesses aren't bad, democracy is a relatively new thing to Europe at large and the easiest way for any woman to survive comfortably up until quite recently was to marry well into high society, and marrying a prince was the ultimate version of that. Taking Disney's Cinderella as an example, how else was she going to escape her situation? Run away? In what looks like pre-revolutionary France? She would have ended up in a brothel, as a scullery maid to an even worse person or just dead in a ditch. And she would have lost all her friends and her childhood home in the process. Also, her relationship with her stepmother was a pretty clear example of extreme emotional abuse and a quick look at the narc threads over in Relationships will tell you how hard it is to just cut and run.
Being a Disney princess doesn't automatically mean the character is devoid of any worth to a girl watching. Merida and Belle are quite strong yes, but they all have their good qualities. Snow White is nurturing and firm with the dwarves, Cinderella is all about keeping hope in a horrible situation (very useful if, like me, you grew up with someone who drove a steamroller over your sense of self-worth) Ariel is a risk-taking idealist etc.
If you find the films and the merch a bit dry, might I suggest Amy Mebberling's Pocket Princesses series on Tumblr? She draws little comics of them all living together, it adds a lot of depth to their characters and it's downright adorable. I especially loved how she dressed them all up as past and present Doctor Whos.
amymebberson.tumblr.com/