>My use of "your" idea doesn't exclude your use of that idea

It can and does exclude me from certain uses of that idea. For example, if my intended use of that idea involves profiting from selling a good/service incorporating that idea, but my target customers decide not to buy from me specifically because you are using that idea. Sure, I can still use the idea in many other ways, same as you can use your land for many other things even whilst my sheep are grazing on it, and what was your wood for other things even after if I've burnt it to ash, but your use of my idea has reduced its value to me. All property is monopoly rights over something, and yes, all forms of property rights can be abused; that in itself is not an argument for their elimination.