You forgot the most important reason they're used: they're far more powerful!

My favourite thing about air tools was not having to worry about batteries (most electric hand tools I've used are battery only so no opportunity to use an extension lead like you use an air hose)

The motor also doesn't create sparks so they are more useful in flamable atmospheres.

Most electric hand tools are usually available for cheaper in a corded variety. The only electric hand tool I haven't seen come corded are impact drivers and most impact drivers I've used will last a day or two using it 8 hours a day even off a 2aH battery.

For me, I like air powered tools because of their power and reliability. They'll almost always have more torque and power than similar electric tools.

Air tools defintely don't have more torque than electric tools, they rely on speed to overcome their shortcomings in torque. The main high torque application in air tools is in impact wrenches, which use very fast hammering action. Modern battery impact wrenches can match the performance of the best air wrenches.

A top of the line M18 fuel impact (a $300 tool, before the $100 battery) is only equivalent with its air analog on the 1/365th of the year shop pressure runs at 90 because the OSHA guy is poking around and it's a heck of a lot bulkier.

When you start getting into 3/4 and 1" it's not even a comparison.

The cordless is nice to have but it's a luxury/convenience tool, not a replacement.