Why aren't thin, delta-shaped wings used for fighter aircraft?
Yes, it is. It was used on may 2nd generation designs already mentioned by habu, and it is returning now in the 4.5th generation, now with canards:

Eurofighter Typhoon:



JAS-39 Gripen:



Dassault Rafale:



And occasionally without too:

HAL Tejas:



And most of the other designs, while having horizontal tail surfaces, are not really far from that layout either:

Mig-29 (Su-27 looks very similar and all the newer Russian fighters are derived from either of those two):



F-18 Hornet:



The F-22 and F-35 with their negative sweep trailing edge are more of an exception, their layout being governed more by requirement for lower radar cross-section than aerodynamics.