They aren't using Patriots on Shahed drones. There are much cheaper purpose-built systems for that. While not practical everywhere, helicopter gun systems have proven effective in both the Middle East and Ukraine.

APKWS is quite popular and those cost less than the drones. A single fighter jet can carry 40. The Europeans are developing equivalent systems.

While not widely deployed yet, the US has operational laser-based anti-drone systems that have been shooting down Shahed class drone for a couple years now.

Ballistic missiles are more costly to deal with but ballistic missiles also cost much more.