If Bitcoin keep the system, we never see the price rise. Many people will get their Bitcoin easily by mine but Bitcoin will not be like today. The scarce is the thing that make Bitcoin priceless and makes people chase it.
The ordinary computer can't mine because the algorithm change and needs specific hardware to mine. The difficulty change timely so ordinary computer can't solve the difficulty.
The scarcity in this situation would continue, there is nothing that we can do about that. We need to realize that we can't really consider this as a big deal. Think about it: the miners would still mine, it would just be different miners.
Instead of huge companies with insane bitcoin mining farms, it would be all of us equally farming with our pc if we want to. And that means while the hashrate would be lower, it would mean instead of 10 companies ruling the entire landscape, we would have tens of millions of people making smaller returns, but good for regular people. Think about making like 10 dollars per day for having your PC open. Now that is not good enough reason to have a PC and open it, because electricity would probably be that much at least. But if you already have your PC open, then why not?