How does the "follow-me" solve heavy delivery?

Heavy deliveries will always be a problem. It existing doesn't invalidate usefulness of things that solve light delivery.

Really heavy deliveries will be. A system that lets you specify a certain weight cutoff for location to deliver might be useful, but even then sheer quantities can be an issue.

I get anything valuable coming from a major delivery service (DHL, FedEx, UPS, US Postal Service) sent to my office. They're already stopping there (it's a hospital with plenty of doctors' offices in their attached tower, lots of stuff is delivered daily), someone can sign for it and lock it up. I have a key to get into my office whenever I need to, and if it's during the day I can borrow a cart or a dolly/hand truck to take it to my car. Can usually rustle up a spare cart even in the off hours. Done it for almost 20 years.

If it's a TV or something else large (appliances, furniture, etc.), it's going to be a custom delivery anyway, so I'll pick a time that I know I'll be home.