An argument can be made that copyright and patent worked before the digital era.

The trick that Claude Shannon introduced may have been intended to remove noise, but that's not all it did. Digital encoding allowed data to be repeated indefinitely. Put another way, data was scarce when it gains noise (lower s/n) each time it is re-amplified; Shannon's encoding schemes allowed perfect copies, and thus data was no longer scarce.

> copyright and patents exist exactly to create artificial scarcity

Copyright and patent cannot create scarcity, nor were they intended to. They rebalanced existing scarcity.

Also you're right, patents and copyrights are not there to create scarcity - an IP owner can use a license that allows absolutely everyone to use it. They exist to give the owner a timeframe with which to recooperate costs of IP generation (and yes, the copyright timeframe is too long but patents are reasonable).