Historically prices of futures never influenced the price of the underlying asset much.
Also, keep in mind that a future is originally meant for commodities like e.g. grain or wood. These contracts are passed on like hot potatoes, because if the contract expires, you literally get your commodity delivered in your front yard. Most people don't want that but.... because bitcoin is digital and it would fit nicely in any backyard worldwide with virtually no transport or storage cost, it is very easy to take delivery after the future has ended. My guess is that shorters will be terribly burned, soon.
How can the price go down on a limited resource ? Eventually a shorter must buy BTC to pay back the BTC that he/she borrowed (that's how shorting works). But BTC is getting more rare every day. In every dip on the markets, there is some farmer in zambia who bought his first bitcoin. Since there are a lot of farmers left in zambia without bitcoin, the transfer is still going from the few to the many, and no future contract can ever prevent that.