Doesn’t a Performing Rights Organization like ASCAP or BMI already collect all my worldwide publishing royalties?

No. Performing Rights Organizations such as ASCAP and BMI collect performance royalties worldwide, but there are many other types of publishing royalties they don't collect.

Things your Performing Rights Organization doesn’t collect include:

• All mechanical royalties from Spotify, Apple Music and other streaming sites. These are generated from every single stream.
• All international mechanical royalties from download stores like iTunes. These are generated from every single sale.
• Global YouTube Sync Publishing royalties for any video on YouTube that contains your song.