EDIT: In case it's not obvious, the fact is that most people don't type the website address in the URL bar. They type it in the Google search bar.
The effect is that people have to now remember two generic dictionary words. "burrito" and ".catering", or wait, wasn't it "tacos" and ".food" or something? And like you said, I'm sure most people don't even recognize that ".catering" is a TLD, whatever that is, and the domain name just looks like `<genericword>.<genericword>` making it all the more confusing and arbitrary.
It's like having to remember where the periods went in "del.icio.us" and, if you couldn't, googling "delicious" (until it caught on) was incredibly unhelpful. Just like googling "burrito catering" doesn't necessarily take you to "https://burrito.catering".
I think even a random brand name + ".com" is still preferable to most of these new TLDs.
Like Qdoba, choose something unique. The domain caterrito.com is a little overspecific, but memorable, unique, easily trademarked, and available.
All we need now is to create a syntax for "internet identifiers" which is instantly recognizable as such. Enter ... drumroll ... @burrito.catering?
The choice of generic words like "burrito" and "catering" is a marketing decision. The original example was mostly a placeholder.
I've also tried explaining to her that the address box doubles as a search box, but she still goes to google.com to search. ¯\_(ツ)_/¯