Actually, my DS is now 15, so that's not an issue. When he was younger, we all went up together. He selected his food, I served it (I hate it when kids serve themselves, btw), & my DH held the plate. Sometimes, I did both. I didn't feel like we posessed super powers to be able to accomplish that. If you have more kids than adults, I can see things would be different.
As for carrying plates..... At TS restaurants, the server delivers drinks & plates. Usually a busboy cleans them up. If the family doesn't order appetizers or desserts, the buffet server could end up clearing away more dirty plates than the TS server brings. They also bring your drink. If we choose to eat a restaurant where we have to serve ourself, that's not the servers fault. They're still having to deal with our dirty plates, which IMO is worse than delivering fresh plates.
And your Spa analogy..... Was I supposed to see a correlation between that & TS vs. buffet dining?