I believe there might be one more advantage that Stranger did not list, but did address. I was told that canard designs make especially tactical aircraft more agile with a greater climb rate in addition to being more stable. A stable platform is vital for firing guns according to Chuck Yeager; a small wiggle in the wings while firing can cause a huge variation at a thousand yards where fighter pilots are often aiming.
As Stranger mentioned, F16’s can already make 9G turns- that is as tight as almost any pilot can endure (and more than they can sustain for very long) so additional flight surfaces are entirely wasted. The F15 and F16 for sure have a greater than one to one thrust to weight ratio (in the right configuration of course) and I have personally witnessed an F15 pivot from horizontal to vertical flight in about a nanosecond and blast into the stratosphere with full afterburner like a booster rocket. I am pretty sure the F18 Hornets and Super Hornets are also greater than a one to one ratio, but not fully loaded because they have much heavier landing gear and a large payload.
The one tactical aircraft that might have benefited from adding canards already had one of the most complex system of flight surfaces, the F14 Tomcat. They WERE front heavy, and just heavy! (They are no longer in service, retired quite some time ago.) They had a lot of thrust, but they also weighed a lot. They already had the variable geometry wings which adjusted automatically (in at least some situations if I am remembering correctly but it was still one more thing the pilot had to keep track of). They were not very agile by most accounts, but their role was as a standoff Fleet Defense weapon that carried missiles that had a range of about 135 miles with three different targeting systems as well as other shorter range missiles. They did not turn very tight and that would be a distinct disadvantage in a genuine dog fight, and as mentioned above they were very nose heavy.
Years ago I watched a training film or documentary about aviator training and all of the pilots said they trained mostly against each other and since all the similar aircraft had the same turning radius, the trick to a victorious encounter was to get your opponent pointed down while you were going up. Once that happened you could literally just get behind them and drive them into the sea as they turned in ever descending circles to stay ahead of your guns. Once you are spiraling down in aircraft that turn at the same rate, the flier who is higher and behind HAS to win the encounter.
But if one of them had canards in otherwise similar aircraft, they could out turn and out climb their opponent, a huge advantage. If you can out turn and out climb – you no longer have to spiral downward to stay ahead of his guns. Even if you are spiraling in with the other plane behind and above you- you can make a short dive to build up airspeed then pull back hard and climb at a rate that would never allow the other guys guns to be pointed at you. What is more, since you turn tighter, you could loop around and come in behind him causing the hunter to become the hunted and then he would have to perform evasive maneuvers to avoid your guns. Once you are behind the other aircraft that cannot turn as tightly as you can, you can drop back a bit and (no matter what attitude you are at) use the canard assisted lift of your wings to put a burst out where he will climb into it momentarily. As long as your wings are parallel to the other aircraft, you can pull your nose a little higher than he can and then it is just a matter of timing the burst to hit before he changes direction. The canards would also help you dive more rapidly so that could be used if he instead dives to avoid you.
The tricky thing about canards is that all three sets of control surfaces must not align in level flight or they will interfere with each other. Just like your main wings and rear stabilizers cannot be in the same slipstream, the canards must also have uninterrupted airflow that does not disturb the airflow of the other surfaces under any circumstances. That by-the-way, is why so many tactical aircraft have twin tails I am told. In a steep climb a single tail can become entirely hidden in the “shadow” of the cockpit bubble. In flat, level flight airflow streaks along the canopy and flows over the tail smoothly. But once you start jinxing around the airflow over the tail might be disturbed so they put twin tails outside the profile of the canopy so at all times one or the other (and mostly both) will have smooth airflow over the surface area.
Disclaimer: Even if I have remembered this perfectly accurately, the information is twenty years old or so. Watching aerial demonstrations of the F22 have convinced me the aircraft I so admired long ago are woefully inadequate against top of the line modern aircraft. (It is however, my opinion that any of those older planes mentioned above, any still in service, is a match for the F35 which is a dog in this guy’s view.) Ducted thrust is an amazing technology that beats even the most rakish canards in real life it would seem.