Odd trademark registration requirement?

A client came to me for a second website because his trademark attorney said he MUST have an e-commerce site using the same phrase as the trademark he wants to lock down.

This seems bonkers to me since trademarks were registered long before the internet was a thing, and he only has one item to sell. (His main site is about services he offers, a bio, etc.)

I'm happy to create a second site for him, but feel that he's getting strange advice. (Or not correctly understanding what he was told.) Any thoughts?

Location: Los Angeles, CA