Almost every patent depends on a prior invention. If the invention is a material object, it probably depends on metal or plastic production techniques, chemical engineering, and other steps necessary to its manufacture. If the invention is the use of an algorithm on a computer, it depends on the many pieces of technology that are necessary to build a computer. It wouldn't make any sense to prevent patenting an invention that cannot be realized without other technology.
It is in fact perfectly permissible, and routine, to patent improvements on previous inventions. For example, a cheaper manufacturing process, or a smaller device that was previously known to be possible. In the United States, the applicable law (USC 35 §101) reads (my emphasis):
Whoever invents or discovers any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof, may obtain a patent therefor, subject to the conditions and requirements of this title.
There are several flaws in your reasoning. One is that there is no such thing as “the patent for touch screens”. A patent is granted on a specific method for achieving a result, not on the result itself. A touchscreen is a result: an apparatus that both displays images and reacts to the touch of a finger or stylus. There are many ways to accomplish this result (e.g. resistive, capacitive, etc.), and each of these is likely to be covered by many patents that concern a small part of the device or its manufacturing process.
A second flaw is that even if person A held a patent covering a specific use of touchscreens, it would not prevent person B or anyone else from using touchscreens for another purpose. It is practically impossible to patent “all obvious uses of touchscreens”. For one thing, if it's obvious, it isn't patentable. Assuming you really meant all the uses of touchscreens that anybody has thought of, that's a tall order. Once again, a patent would have to cover a specific use of touchscreens, for one specific purpose. It does happen sometimes that a company can effectively “lock” the use of a technology by holding key patents related to that technology, but even then what it usually means is that the alternate ways to accomplish the same result, while known, are more expensive than paying royalties for the best method.
In the specific case of two Apple patents related to multi-touch screens, these patents cover the use of specific gestures to accomplish specific results (a particular way to scroll or zoom). Even if the patents are valid, they would not cover any method to scroll or zoom using multiple fingers on a touchscreen that does not follow the precise sequence of steps listed in the claims, let alone the use of multi-touch to do anything other than scroll or zoom.