Why does the Deep Space Atomic Clock have such a short mission?

It has a short mission because it's a test, or in fact a technology demonstration mission, not a production system. The idea is to show that the thing can be flown and will work. Once that's done it serves no purpose any more. From this page:

The clock's in-space mission will validate its stability in orbit, fully characterize its long-term performance, and demonstrate its capability as a navigation instrument.

Once it's been shown that it works, these clocks will be used on non-demonstration missions. This mission may also be extended if is usefil to do so. Note that the system won't be like GPS where there are lots of clocks on lots of satellites: rather a mission to Mars, say, will carry a really good clock with it, and this will enable it to know how far it is from Earth, say by comparing its time with the time stamps of signals received from Earth. Currently that is done by measuring the round-trip time (Earth->spacecraft->Earth) and this obviously takes a long time. A description of this is here.