Isn't that what we've got airstrikes for? The downsides of using artillery and using airstrikes is that explosives also destroy the alien gear with the aliens. Gear that you need unharmed, either so you can sell or study it. Also, why would you use artillery in the same area as your soldiers? Fights tend to happen in a small radius around the UFO, a radius that both the aliens and your men will be in. I'm fine with fire support coming from MGs, tanks, and rocket launchers. I think infantry rocket launchers are a lot more effective then artillery would be, because they're more manueverable/selective, less destructive to alien technology, and a lot faster to call in despite their low ammo capacity. I guess you could bombard the area around the UFO before sending your men in, but why wouldn't the aliens just hide in their UFO? Also there's the matter of property destruction and civilian casualties.