In a "normal" environment, it doesn't make sense to me that wealth begets more wealth passively without doing anything:
A) If your wealth is in cash in the bank, you are providing the bank with deposits. The bank can now make cheaper loans which helps others. But if these loans default, your bank fails and you get bailed-in. Assuming no government intervention comes to save you.
B) If your wealth is in stocks or corporate bonds, you're helping to finance companies that are making stuff / providing services that people might need. But markets can go down, companies fail, and as long as there's no bail-outs, you should be able to lose it all.
C) If your wealth is in government bonds, you're obviously financing the government. But if there's no buyer-of-last-resort (central bank) for your bonds, then one dodgy policy decision by the government, a large bout of deficit spending, or a failed bond auction will wreck the value of your bonds.
D) If your wealth is only in stuff, land etc. then your wealth shouldn't grow - in fact it should fall as these deteriorate in quality, and you're taking a big hit in the form of opportunity cost by not doing anything productive with the land/stuff. If you're having to maintain this 'stuff' then you're losing money, think cost of ownership, replacing capital etc.
E) If your wealth comes from rent, then you're taking a risk, and expect costly demands from tenants and to have to keep up with a competitive market. This I accept is something of a grey area because uncompetitive markets / monopolies can exist.
F) If you're wealth is in patents, copyrights fees, royalties etc... then there may be an argument here. This is up to the government to change, similar to E but without as much risk.
The trouble with the above A-E is the inherently inflationary system we have now where markets are never allowed to go down and deflation, bank failures, and default is prevented with stimulus. It props up stocks, bonds, means assets and stuff gets more expensive nominally without doing anything, it keeps banks afloat and means bail-ins of depositors are unlikely. Rich people who acquire assets are on to a guaranteed win like you say.
The solution is not to take away the incentive to produce more wealth by a punitive income tax, but to take away the asset inflation that makes asset holders rich by doing nothing, which also makes cash holders poorer and punished for being prudent with their meagre savings.