The greeting says "You don't really have a house so these items have no use, yay!"

We players don't have houses but the fictional world of Subeta has human and humanoid inhabitants. They need cookware, toilet paper and other things sold in this shop. ( I don't know why any of them would want a broken lightbulb, though.)

Could the greeting be changed to something which fits in with the fictional Subeta world?

Maybe they don't really have a house either?

I actually really like how sassy the shopkeeper is. I don't have a strong opinion either way

I now have a bizarre image of Sagittarius along with the other Subeta Council members and the rest of the human and humanoid population going behind bushes and using leaves because there aren't really any toilets or toilet paper. Members of the Subetan monarchy who lived in the King's Quarter of Centropolis would have had fancy topiaries to go behind. :D

Isn't it a really old reference to how there's houses on Neopets but not here?

Yes, it is a reference to Neopets but I don't think it fits how Subeta has developed over the years. There was a big effort made to give the fictional world of Subeta a history and develop the NPCs as real characters.

The Centropolis location on Explore shows a modern city with modern cars. Home Appliance products would definitely have a use in this fictional world even though players can't build Neopets style houses and furnish them.