These drones won't be that much cheaper. The life support isn't the most expensive part in high performance fighter jets, it's the airframe, sensors, and engine. The airframe will still have to have some sort of stealth and the engine will be similar to those in other fighters, especially if they're expected to be supersonic too.
A single sidewinder is almost 200 pounds and GBU-31/32/38 JDAMs are 500-2,000 pounds each, so accounting for the pilot and ejection seat, you're only getting a small bomb's worth of weight.
Making them smaller significantly reduces the volume available for weapons, sensors, and fuel too much IMO. See the Predator, which doesn't have a large weapons loadout and still has the cockpit dome for the radar.
Not necessarily, there is a balance to be found. For example, there is no point sending thousands of mini-drones if a simple jammer can make them all fall out of the sky, or if they can't reach their target because their range is too limited, or because they are too slow and visible for a surprise attack.
Modern fighters are big and expensive because of their capabilities like speed, range, stealth, weaponry, counter-measures, radars, etc... And they are not just made to blow up stuff (we have missiles for that), they are also complete platforms for reconnaissance, communication, etc... And the pilot is not just there to control the plane, he is also an officer on the battlefield with all that implies regarding situation awareness and decision making.
The F-16 was original meant to be cheap, not even having a radar. But by the time it reached production it had far more equipment and weight, for better or worse.
It's original designers thought we should have 10x the aircraft in the sky for the same price. This would result in more fighter pilot deaths, but, as callous as this sounds, maybe that's okay? I mean, it's funny how much expense will go towards saving the life of a fighter pilot while soldiers on the ground can't get proper armor on their vehicles.