The cannot own houses, factories, monopolistic contracts o media. It makes harder to influence politics ( in a legal way).
The housing issue is specially important because city space is limited and the demand is very inelastic
People can own houses, factories, &c, in indirect ways, or in other jurisdictions, and these are all basically legal and make it hard to say what, exactly, people own.
The easiest people to tax are people whose inflows are simple wage income, who own a house and a car in their own country, and don't have a business. In other words, ordinary people. They make up a bulk of the financial activity in a country and the bulk of the tax revenues (most of the time).
It is easy to imagine that the way to capture greater tax revenue from wealthy people is simply to scale this system up -- tax the wealthy people more on their income, their expensive car, &c. However, wealthy people are also wealthy in structurally different ways from ordinary people.
This is, I think, another example of people's intuitions about tracking wealth just not being very robust.
There isn't anywhere an index or lookup table of all legal rights a particular person has to wealth (or, in truth, to "things", since anything can be worth something and contribute to wealth). There are things they may have a right to that they don't even know about.