That is what a lot of countries have. In places like Mexico and Panama and Ecuador and Thailand and Malaysia, getting a visa requires having a certain amount of assets in the country, or proving a guaranteed income, such as a pension, over a certain limit. Panama, for instance requires $500 or an investment in a house or condominium over $200,000. And you must renew every year and prove you still have the income and the property. I think Mexico requires $1300 per month.

When all the 'free to work anywhere in the EU' came in, it was a good idea. Countries had to meet strict economic criteria to get into the EU in the first place, and there were only a few (Spain, Portugal, Ireland, and Greece) that had poor economies. So it allowed the free flow of people around countries of relatively equal wealth. The economies in the poorer countries picked up, and it worked well. However, taking all those eastern European countries in at one time really upset the balance of labor and social services.

People still flood into the US, and we don't offer much of anything in the way of social services, and make it pretty hard to get in, at least legally.