Allocating ones capital (simply owning things as you say) is a productive activity in itself. Without people competing to allocate capital for higher returns, a lot of things we all love wouldn't exist.
People should own what they create (organizations, buildings, goods, and services), but the natural geography of the world should belong to all. If one wishes to lay claim to a stretch of land, and prevent all other equally born humans from entering or making use of that land and its resources, one should pay a tax to society for that privilege.
As you say, "people competing to allocate capital for higher returns" is a great thing. However, I dispute the fact that some people should even have the right to decide how to invest their land without first paying a societal price for it (much higher than current land tax levels--high enough to cover a corresponding decrease in most other taxes on labor or production).