LTP, no your suggested "solution" would not make me happy. To suggest such an idiocy makes you sound very petulant. It is not a solution because it does not provide an improvement on what we have now.
No, Class G airspace is not "see and avoid". Those are the rules for VFR flight. There is a difference. You may like to look them up. While you're about it, check up the rules for flying IFR as well.
If a military jet is flying VFR in Class G airspace, the onus is on the pilot to ensure he is as well-informed as possible of other traffic using the airspace, and to see and avoid them. Failing to talk to ATC to inform himself of that, failing to use all means at his disposal to prevent accidents that may be caused by his playing with his mates is lack of professionalism.
Military controllers who refuse perfectly valid requests for information from the civilian colleagues about the likely intentions of military aircraft under their control also display similar lack of professionalism.
Civil airliners are as entitled to use Class G airspace as the driver of an FJ. At present there appears to be a singular lack of professional courtsey and responsibility about its use on the part of the military.
By your own admission airspace does not meet the needs of either the military or civilian operations.
It's time for a rethink.