I'm with you on the suspicion that Zaofu seems too good to be true. But I doubt that the entire city is based on thievery.
During dinner, Suyin expresses a fundamental philosophy of hers: "Sure Varrick's made a few mistakes in his past, but that doesn't mean he should pay for it for the rest of his life. My chef was a pirate, but now he's a culinary master. People change.". To me, this implies that Suyin has a very clear moral concept of right and wrong. She believes in the good side of people and in second chances. This would clash with the idea of stealing from other cities in order to finance her utopia.
If she were to steal the taxmoney of surrounding towns and cities before it could be collected for the Earth Queen, she would just collect more taes and the people of said towns and cities would suffer as a consequence. Unless of course, the stealing would continue indefinitely and some of the stolen money would be returned to the citizens of said town or city. The Earth Queen would probably not tolerate this and in the end, the citizens would suffer again. This hardly sounds like something Suyin would willingly accept.
You do bring up an interesting question: how does Zaofu's economy work? Being the utopia that we saw briefly in the last episode, it might very well be that it is very different from, say, Republic City - or any other city for that matter.
In a classic economy, every individual or entity has some money and strives to get more money by exchanging goods and services with other members of the economy who need them. They strive to make profit. Money basically exists because neither party trusts the other.
Maybe Zaofu has done away with money for internal use. Maybe the entire community is built upon the concept of honesty and empathy and doesn't rely on money for the exchange of goods and services within the city. If one entity can provide a service for another entity in Zaofu, they do it for free in the knowledge that in the reverse case, the same will be true. Goods are handled similarly. Nobody takes advantage of this system because of the Truth-Seers like Aiwei, who would be able to detect dishonesty and greed.
Money would still be used for the trade with outside sources. Or how else did Suyin's chef get his hands on wild Kyoshi elephant koi? But again, this money is used by the entire community of Zaofu and not individuals to bring in external wares for internal consumption.