During the era of empire waists, women were actually wearing corsets!

There's a short period of time where corsetry was really in transition, and some (highly fashionable, typically elite) women may have gone without any foundation garment - from roughly 1795 to 1805. A lot of primary sources talk about women just wearing lightweight linen bodices of some kind, and we have a number of interesting garments that are generally made like eighteenth-century stays but cut to go under the bust rather than hold it up. These latter put tension on the shift/chemise to give some stability (while also slimming and shaping the waistline), while the gown - usually cut during this time to have a lining that pinned together in front - provided some more, while all together keeping the "natural" silhouette with a curved bust.

By the late 1800s, fashionable women were starting to conform to a more standardized type of corset, the one stereotypical of the Regency period: essentially tubes made to flare out over the hips and around the bust with triangular gussets inserted in strategic places. Something more engineered was needed than the lightweight or underbust transitional corsets, as the fashionable silhouette called for the bustline itself to be raised so that the high waist could be as high as possible. (This is often misunderstood as being done to create a lot of cleavage, leading people to think that certain types of modern bras can be used to get the same effect in a costume; unfortunately, modern bras don't push the bottom of the bust up and create the 1810s silhouette.) Now, these corsets ... actually look so much like corsets of the 1820s, 1830s, and 1840s that it's really difficult to date them! While the fashionable shape above the gown was willowy and high-waisted, the corset itself generally had a defined waist, because wearing a corset without a waist would actually be quite uncomfortable! And while the popular stereotype is that women started tight-lacing in the 1830s because the return of the defined waist in fashion made them all crazy, concerns about tight-lacing (in all periods) have a lot more to do with contemporary concerns about women, vanity, self-destruction, etc. etc. than actual tight-lacing going on. Very, very few women seriously tight-laced to the extent that modern-day tight-lacers do. The change that occurred in the late 1820s was mainly in the outer dress than in the body beneath.

But that still leaves the question of why fashion went back to a waisted silhouette.

One reason is that fashion generally goes in cycles, with new features being added for the fashion-forward to distinguish themselves with, then increased or exaggerated as the features trickle down to those outside the ton, then decreased or eliminated to set those in the know apart from those who are copying them. By the 1820s, the high waist had been around for more than a decade, and it was time for it to come down again; the narrow skirt had been belling out slightly for some time and continued to increase, and sleeves were swelling. The waist would continue to move around, though it would generally do so more subtly.

Another is that the dominant historical influence on fashion changed. During the 1790s and early 1800s, fashion was all about the imitation of Greek, Roman, Etruscan, and Egyptian forms, particularly (when it comes to silhouette) the look of Hellenistic chitons. While English fashion clung to the slim Neoclassical look through the 1800s and into the early 1810s, more recent historical influences were generally becoming more popular: Gothic (medieval), Rococo (eighteenth century), and Van Dyke (seventeenth century). These styles were more inclined to full sleeves balanced with a full skirt, and while they started subtly, they eventually took over and ousted the Neoclassical look entirely.