What prevents fighters from being fitted with jetliner-style bleed-air wing anti-ice? In a comment, John K points out that:

In any case, military fighter aircraft have to avoid icing, which is kind of odd for those that are considered &quot;all-weather&quot; interceptors..

This, to me, raises the question of &quot;why would you omit wing anti-ice from a supposedly 'all-weather' aircraft?&quot;  Especially on a larger fighter like a F-15 or Su-27, it seems to me that the weight penalty for a couple of piccolo tubes, two butterfly valves, and a bit of extra bleed ductwork would be fairly minimal relative to the weight of the aircraft and payload, or am I wrong on that?  Or are there aerodynamic or engine-performance reasons that prohibit fighter jets from using bleed-air anti-icing, or some other anti-ice system for that matter?  I've also heard the saw that &quot;fighters don't need anti-ice because they can simply fly fast enough to use ram rise to deal with icing&quot;, but could there be other reasons they couldn't fly in icing, such as not having heated pitot/static systems or inlet anti-ice functions?
Most fighters have enough thrust to power through icing conditions, so anti-icing or heat is limited to inlet(s) and pitot probe(s). That said, at least one F-16 flight manual, to use one example, says the following about flying in known icing conditions:

Flight in areas of icing should be avoided whenever possible. If icing
conditions are anticipated or cannot be avoided, turn ANTI ICE switch
to ON and PROBE HEAT switch to PROBE HEAT. Frequently check the
aircraft leading edges for indication of ice buildup. Make all
throttle movements slower than normal when in potential icing
conditions to reduce possibility of engine stalls and/or stagnation.
Consider diverting to an alternate field if required to avoid icing
conditions.

The F-14 also had the same systems, engine inlets and pitot probe heat. No other anti-icing systems on the aircraft.