Every object moving through a fluid will heat up, both by friction and by compression of that fluid at and around the stagnation point. Jet fighters heat up enough already that it is not necessary to put de-icing devices on their wings. The temperature at the stagnation point goes up with the square of velocity, therefore the heating becomes quickly problematic for common aerospace materials like aluminium once the top speed grows above Mach 2. The MiG-25 used steel and the SR-71 titanium to enable their structure to suffer the heating from Mach 3+ speeds.
In supersonic flow, the air has no indication of the approaching vehicle. The first contact will cause a sudden change in direction, called a shock. For drag reduction it is important to make the shock as weak as possible, which means that the change in direction should be as small as possible. This can best be achieved by a slender, pointy tip.
In hypersonic flow (Mach > 5) a blunt nose might again be preferable if the nose's materials put an upper limit on aerodynamic heating. A pointed tip will produce an attached shock which will heat the tip to something close to the stagnation temperature of the flow. A blunt nose, however, will cause a separated shock. This creates more drag and higher heat loads overall, but allows to spread the heat over a larger area and produces lower peak loads. The Space Shuttle had such a blunt nose, since drag minimization is not a priority for a re-entry vehicle.
Jet fighters have indeed better aerodynamics because their heating is still low enough to afford pointed tips, and the poorer aerodynamics of reentry vehicles is caused by the need to limit peak heat loads. When the Shuttle was designed, the military desired to maximize the distance the craft could glide during reentry (called cross range), and sufficiently good aerodynamics were only possible with the newly developed thermal tiles.