Why don't all aircraft have them? Well they're noisy, they make a hell of a mess, quack all the time,...
Stupid remarks aside, the benefits of canards are not as cut and dried as Fresca states. There are a number of factors which reduce their attractiveness:
1.
Canard produces lift, while h-stab produces "anti-lift" i.e. downforce. True up to a point, but of course the ideal situation for cruise is no trim lift force at all, because the wing is the most efficient lifting surface. And there's no reason why I can't have true lift on the aft surface, if I'm prepared to consider active controls (to cope with aft c.g. movement), which are common on canards of a certain kind anyway. Even without active controls I may have an aft enough c.g. that the h-stab generates lift.
2. Canard behaviour in stalls/high lift regime. Well, here we certainly see a down force on the aft surface, so the h-stab is losing lift, while the canard is adding lift. Unfortunately, the surfaces do not act in isolation. All the lift generated by the canard (or any other surface) will manifest as downwash; this will reduce the effective angle of attack on any further aft surfaces, which will reduce lift. Additionally, this downwash field will be concentrated over the inboard wing, assuming it's a canard-wing configuration and not two wings, and so either you have to account for significant variation in the flow between inboard and outboard wings, or accept a non-optimal flow for the wing. The whole canard/wing interference can seriously mess with the apparent trim lift gains of the canard configuration.
Regarding the pitching moment behaviour - the same can be achieved through good wing design and/or systems devices.
One thing canards are good for is flexibility in placing surfaces around the aircraft. If the aerodynmaic effect for lift is neutral, then I can choose the configuration which is better for drag. Canards, especially canard-deltas, lend themselves naturally to a good area distribution, while the aft-tailed configuration struggles to achieve as good results. That's an important consideration for the European latest generation fighters.
Basically canards are just another configuration; there are benefits and disadvantages to them (just as with things like FSW). Some design requirements are best met by them, some are not.