Manufacturers specify this fairly conservatively. They must do so, because they have to assume that some of their derailers will be sold to incompetent cyclists, who will abuse their drive trains by using the smallest chainwheel with the smaller rear sprockets.
Competent riders can considerably exceed the official rated capacity, since they will not misuse the granny ring by running it with the smaller rear sprockets, so it doesn't matter if the chain hangs slack in those gears.
Rear derailers are also commonly designed for a particular maximum size rear sprocket. If you exceed this size, by too much, the jockey pulley may rub against the sprocket when using the lowest gear.
Rated maximum rear sprocket size, however, is also commonly much lower than what actually works. For instance, Shimano's models designated as "road" derailers are generally listed for a "maximum" sprocket of 27 teeth...because 27 teeth is the largest size that they make in a designated "road" cassette. However, in almost all cases, these derailers, even the short-cage models, will handle rear sprockets as large as 30 teeth in practice. (This somewhat depends on the design of the frame's derailer hanger, so once in a while you will find a particular installation where you can't use a 30, but I've never seen one where a 28 wouldn't work.