It’s unfortunate when we don’t get picked for the dodgeball team. Life is inherently unfair and mostly a lottery.
(not against foreign aid charity by any means, but delivering it distinct from immigration policy is potentially more efficient and optimal in many ways)
Maybe those wealthy immigrants are very talented people who are very good at, say, managing an insurance company or researching pharmaceuticals, but Japan has a glut of 55-year-olds who can do that stuff very well. They're running short of young people who can be nurses, junior machinists, and construction workers.
In a macroeconomic sense, wealthy people might be able to pay for the services they need from their own pockets, but functionally it's not that different than being unemployed (unless they choose to work). They would be almost purely adding demand to the economy. The wealth they are bringing represents supply that they added into the economy in the past and abroad, and now they have a wallet full of paper with which they can buy services for the next 30 years in Japan without having to do any further productive work.
Sweet deal.
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.
It's absolutely more likely that the very wealthy that aren't taking as many risks in moving to Japan are not going to care about Japanese culture.
Furthermore, it’s deeply disingenuous to suggest that inconsiderate people only exist on the upper end of the income distribution. Assholes who want to take over and control others are found at every income level. If you want to keep your country from descending into Marxist dystopia then making fuck you money a requirement for immigration is not a terrible idea.