Many factors have gone into the changes one sees in not only Amercian but Western European hosptials as well. Changes in the nursing profession, and the nursing shortage has played a major role in shaping how things are done these days. There is also a desire by hospital management to cut costs (or, save money).
In terms of hosptial linen, many changes started when hospitals began to close in house laundries and move to sending their linens to a service.
In my day, learning to make three kinds of patient beds with mitered corners, was standard part of Nursing 101. Indeed one could get very bad marks indeed for a poorly made bed. However today many nurses complain the average American hospital patient is not only sicker, but larger (read over weight),and shifting him or her about to make an occupied bed with corners is difficult to do on one's own, thus requiring two nurses, and even then. So in came fitted sheets, which not only made the job easier, but saved over all time in doing the beds for the nursing staff (including nursing assistants).
Hospitals also began moving away from linens which required laundering, to disposables where possible to save both on linen costs and laundering. As one can imagine, hospital linens can be stained and fouled with all manner and sorts of fluids and medications, that do not always wash out. Badly stained linen must be withdrawn from service and replaced. In the old days pure cotton linens were cut down for bandages and other uses, but those days are long gone. Also the harsh laundering (high water temperatures and high pH detergents, LCB)caused linens to wear out a great deal, this also means increased costs as replacements had to be ordered.
As for "starched whites" and caps, well they pretty much have gone by the wayside in both the States and EU, though have heard about a few places here and there that keep their nurses in at least whites (with or without caps). Oddly one still finds the traditional uniform in places with very strong ideas about a female's role in society, such as Japan, Mexico, and other Asian and South American countries.
Caps went out because not only where they unhygenic (few if anyone bothered to launder, starch and iron the darn things), and the modern nursing profession felt they were a throw back to nurses being "handmaidens" or "servants". Same with whites, as "the Profession" felt nurses should resemble other "medical" professions and wear scrubs or simply a white lab coat over street clothing.
Back in the old days the only nurses who got to wear scrubs were those working on critical care units, or in the OR, or L&D, and even then it was more likely to be OR "dresses" than scrubs. It was sort of like a status thing, since if you went off the unit, everyone knew you were not simply a "bedside" nurse. The rationale for keeping nurses out of scurbs, at least on the floors was that people might mistake them for doctors.
Quite honestly, and one knowns many medical professionals who say the same thing, if one does not have to be in hospital, the better off you are. If you do have to go, stay in only as long as required and then go home. Sadly it seems we've moved back the the old days where one can emerge from a hospital sicker than one was when one went in.