High value immigrants always have value

No they don't. Such a person might use their existing wealth to import goods or commodities, undercutting domestic competitors, extract wealth from the local economy, and then decamp. I'm not arguing that people with high net worth necessarily behave like this, but economic benefit to the host is by no means a given.

For example, the market for vaping-type products in Japan (technically 'heated tobacco') is dominated by American companies (legally) and SE Asian criminal syndicates (illegally). The legal products generate high tax revenue for the government (but not for Japanese tobacco companies) but it's foreseeable that much of the tax benefit will be offset by higher future healthcare costs, while the net profits of the business operation disappear overseas rather than remaining within the economy.