Mike Lee literally authored a bill last year, the "Interstate Obscenely Definition Act", which would ban the transmission of "obscenity" on the internet. He realized that it wouldn't pass muster with the 1st Amendment, so the SCREEN Act is his plan B. It's about censorship first and foremost.
🏳️⚧️ Fiona The Eepiest Kobold 🏳️⚧️People don't realize that this is an existential threat, since censorship will just be easier than requiring identify verification. Mike Lee, the bill author, wants to ban "obscenity", he had to find a way around the 1st Amendment. So, that's why it's "verify ages or get in trouble with the FTC".