There is a super-simple solution to this problem: a progressive tax on income, wealth, and most importantly, inheritance (with an exemption for private businesses below a certain size that are both owned and administered by a single family).
Another possibility: eliminate private ownership of land. This is actually not as radical as it sounds. It's a big shift in mindset, but not that big a change in how things actually work. The mindset shift is to go back to the native american idea that all land is collectively owned by the people. The government is the "management company" that administers it, and one of the things it can do is offer long-term leases. This would essentially be the same as the status quo except that instead of owning the land and paying property tax, you'd own a lease and pay rent. The reason I think this would have a beneficial effect is that the change in mindset would change the dynamics of political debates. For example, NIMBYism would be less tenable because it's not your back yard any more. You're just a tenant.
Another possibility: eliminate private ownership of land. This is actually not as radical as it sounds. It's a big shift in mindset, but not that big a change in how things actually work. The mindset shift is to go back to the native american idea that all land is collectively owned by the people. The government is the "management company" that administers it, and one of the things it can do is offer long-term leases. This would essentially be the same as the status quo except that instead of owning the land and paying property tax, you'd own a lease and pay rent. The reason I think this would have a beneficial effect is that the change in mindset would change the dynamics of political debates. For example, NIMBYism would be less tenable because it's not your back yard any more. You're just a tenant.