Yes, and, again, equity isn't the only form of investment even within the capitalist system (though, obviously, it's often structurally preferred by investors within that system.) So, even granting, for the sake of argument, the need for capital investment to start firms, that does not imply a need for capital, as opposed to labor, ownership of firms. (See, for a large example even embedded within a capitalist economy, the Mondragon Corporation.)
> Property rights are just an extension to help the underlying basics
That's certainly one of the reasons for formalizing such rights, but “property rights” aren't a special feature of capitalism, what defines capitalism—and this is generally true of each other politico-economic system—is a particular model of property rights. And, yes, in each case they are viewed by defenders of the system to “help” the immutable basic needs of human society.
Someone has to pay for the fixed costs. And its most common that an investor does that. Never said it has to be that way, just that it is common and offers many advantages.
> Well, lots of ways, including the thing that actually defines capitalism, the particular model of property rights.
Property rights are just an extension to help the underlying basics I wrote about. If you are a tribe you might life in balance with other tribes and you have control over a river (or whatever) and you might even give something comparable to property right to a member of your tribe. But this is all enforced by society. Property rights are the same thing, just more formalized and generalized. Ofc. there is more insecurity in a autocracy, but that because an autocracy is about exploiting others.