The challenge with "lots of smaller missiles" is really range, I think. You want to hit the target from as far away as possible. That takes fuel, which puts limits on how small you can go.
The longest-range version of the AIM-120 has a range of 160km, and missiles under development promise even longer ranges than that, so that kind of tells you what they prioritize.
One tangential thing to understand is that air to air missiles are proximity fuzed. They don't need to precisely impact their target, they just need to get close.
I think this is mostly because longer range
sounds like a great thing when you don’t have
hundreds of missiles to defend against.
You're optimizing for the wrong thing. Today's missiles are extremely lethal and good at finding their targets. The challenge is getting close enough to launch them without getting killed by other aircraft or ground-to-air defenses. Ground to air defenses are getting cheaper and more lethal all the time.
If you take human pilots out of the equation, obviously this changes things (your aircraft can be cheaper and you worry less about losing one) but not entirely. You still have to figure out how to deliver the missiles without getting shot down and while remote piloting is cool, it's still subject to jamming and such.
Minus the cool swirly anime effects, pilots certainly do have the option of firing multiple missiles at a given target. Fire one missile from beyond visual range, wait, and then fire another one. This is very common in DCS, which is obviously not reality but is a pretty decent simulation according to a lot of actual pilots. Not sure what actual fighter pilot doctrine is there and if that's a real world practice as well.
I was thinking more about Ukraine, not an anime style missile swarm :)
You need defensive missiles that are significantly cheaper and easier to produce to stop your larger adversary from raining death down everywhere.
It’s nice if you have a missile that you can use to intercept any incoming dumb missile anywhere in 300km, but not if your missiles cost 1M and theirs cost 100k.
The longest-range version of the AIM-120 has a range of 160km, and missiles under development promise even longer ranges than that, so that kind of tells you what they prioritize.
One tangential thing to understand is that air to air missiles are proximity fuzed. They don't need to precisely impact their target, they just need to get close.