Why would lead be in the gunsmoke? Everything leaded should be coming out the business end of the firearm, and it should be coming out with some gusto.

The base of the bullet is lead (with jacketed pistol rounds, that's often true even if it's a "full metal jacket" and some brands are trying to draw a distinction there with "total metal jacket" branding) and it's exposed to the explosion when the round fires. There's some vaporized lead, most if it will move downrange and some of it won't. Airborne lead is potentially more of a problem at an indoor range.

Copper, polymer-coated, or total metal jacket rounds will also result in less lead on the firearm, I'd think, and less on the user's hands. One old guy I know who had lead poisoning at one time believes the real risk is getting the lead on one's hands and then handling a cigarette.

Are you proposing that the base of the bullet which is exposed to the burning propellant magically remains at room temperature, and none of the lead in the base of the bullet is vaporized? What about the process of forcing the projectile into the barrel's spiral grooves at very high speed, leaving grooves in the side of the bullet. Where do you suppose that displaced and/or vaporized material ends up? What about the lead styphante that is combusted in the primer? I am not aware of any firearm that has a muzzle filter that removes primer residue from the combusted gunsmoke.

Because the heat and pressure from the propellant and rifling vaporizes or rubs off some of that lead. A very small percentage, granted, but still.

Particularly for unjacketed bullets like 22LR. Even jacketed bullets tend to not be jacketed at the base.

The material that burns in primers is often lead styphnate. This burns and sends lead particles throughout the air.

With rounds that aren't well jacketed like those 22s that are just bare lead, you also get some of the round scraping in the barrels that comes off as dust.

There's tons of lead in the air at shooting ranges.