My wife and I are extensive world travelers with her having a degree in industrial design. We have visited castles, fortress, mansions as old as 1200 AD through present architecture. My grandmother was an interior decorator, working from the 40s through 80s. I have limited primary literature sources, but a range of personal and familial knowledge from both travels throughout Europe, North America, India and China. I report from accumulated knowledge from travels and family professional experience, as well as some limited literature sources.

Chests (of drawers or otherwise), armoires, cabinets (the movable types), dressers, trunks, etc cetera. All of these were used for storage of clothing and other goods before closets and other side rooms became more common. You see depictions of storage of clothing some in Racinet's Costume History, and other literature on the development/evolution of clothing. You answer your own question in a way, mentioning these various cabinetries. The follow-up question: Why don't you see them? Is worth some further explanation.

The growth of wealth in various classes dictated the use of space alongside the evolution of the concept of privacy. I would refer you to one of the many excellent threads on privacy in this sub. In North America, China, India, and Europe where I have traveled and in the professional educations of my wife and grandmother, the answers have been largely the same with differences only in timing of the distribution of wealth and concepts of privacy.

Expensive armoires and other cabinetry was a show of wealth as much, if not moreso, than the clothing itself. You can see some of these decorative works of cabinetry in museums across the globe, some do still remain in situ. These trunks, cabinets, dressers, and the like were used heavily, would travel with their owners, and be passed on to following generations. Thus, few examples remain in place due to damage or distribution. With socioeconomic changes (alongside privacy changes), such cabinetry fell out of vogue, and you begin to see the development of closets. These spaces were initially changing areas but evolved to become clothing storage areas, with some regression/reemergence even to date. Walk in closets were becoming popular again at the end of my late grandmother's career.

TL:DR: Cabinetry is/was expensive, so traveled with the hosts and were passed down through generations. Years/generations of use lent them to damage. Also concepts of privacy evolved favoring closets and separate spaces.

Sources: Racinet's full-color pictorial history of western costume : with 92 plates showing over 950 authentic costumes from the Middle Ages to 1800, Auguste Racinet Dreihaus Museum Tour Materials Chicago, IL 2020 Maison Dauphine Tour Materials, New Orleans, LO 2017 Lyndhurst Mansion Tour Materials, Hudson Valley, NY 2016 Château Dufresne Tour Materials, Montreal, Canada 2015.

If you're interested in seeing specific examples of period wardrobes/etc in place, I can comb through my travel logs with my wife and provide some examples. Hope this helps you understand and answer your question.