Of course you can create a near utopia without taxation for your own people if you are able to import fabulously rich residents by the boatload and taxing them instead. This is obviously not an option that is sustainable on a large scale , nor do most countries have the exotic climate to support it.
In short, you need to tax somebody. In the Caymans these happen to be rich foreigners on holiday (or in some sort of semi-permanent residence)... in other countries clearly the taxes have to come from somebody else.