> However, why is trading existing shares considered "allocating capital"?

Because the company is made of capital. It has a plot of land with a factory, equipment for making brake pads, raw materials, a trade name that engenders goodwill with customers etc. When you buy a share, that share of ownership of the capital is allocated to you. You get a vote in how it's used. You could vote to keep making brake pads as ever, or mortgage the factory to expand into brake rotors, or cease operations and sell the individual assets to the highest bidder.

In principle you could be the deciding vote and someone else could have made a different decision than you.