Why isn't tungsten used in supersonic aircraft?
While tungsten does have a high melting point (I'm not sure what's the relevance of boiling point here), it has little else to offer for aircraft construction. The main issue of course is weight. One of the main goals of aircraft design is to reduce weight while achieving all the required performance parameters and tungsten is among the heaviest elements around, even beating Uranium.

When you factor in its density, it appears less than ordinary- its specific strength is less than 100 KNm/kg, less than half of Aluminum. Another thing is that tungsten is not exactly an easy material when it comes manufacturability. Even its saving grace, the high melting point (over 3000$^{\circ}$ C) is not very relevant as far as supersonic aircraft are concerned. The temperatures experienced in aircraft anywhere other than engines is well within that limit. For example, the surface temperature of Concorde wouldn't even get to a tenth of it.



Concorde surface temperature; image from erau.edu

Surprisingly, tungsten is indeed used in aerospace industry- at exactly the other end of the speed spectrum. it is used as a counterweight for controls in small aircraft and also as balancing masses in rotorcraft blades.