The common thing to do when ringing out microphones is to use a paramertic-eq with a narrow q and notch out the first few problematic frequency's. There are also some feedback-killer products that attempt to do so live.
I think that an all-pass filter would be a better option, leaving the frequency response flat and just altering the phase of problematic frequency's. Offcourse this will only work for static mics that don't move during a performance.
The only reason they are not commonly used, that I can think of, may be that they are just not commonly available. However these days with almost everything digital that could easily change with some firmware updates.
Is there any other reason why they are not used for this purpose?