I came to much the same conclusion independently. The rewards come from the holders of the currency in proportion to the size of their holdings.

This begs the question: why would anyone hold the currency?

You can draw a parallel with Bitcoin: where does the money come from to pay the miners? The answer is that it comes from all the existing holders of Bitcoin, because every block reallocates the percentage of the market cap held by each person, slightly reducing all holder shares and giving it to the miner who found that block.

Why does anyone hold Bitcoin, knowing that their value is constantly being given to the miners? Because they hope that the market cap grows fast enough to counteract the losses due to having to pay miners.

And so that must be the answer for Steem currency holders too. They know that they are constantly losing market share by having it reallocated to fund rewards, but hope that the market cap grows fast enough to counteract those losses.