What prevents fighters from being fitted with jetliner-style bleed-air wing anti-ice?
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.