Otherwise how on earth would you incentivize the network existing in the long-term? Nobody is going to acquire/power/maintain/network/operate these hashing machines if there's no return for their efforts.
Proof of work (bitcoin) will always have them though. The lower bitcoin price will just wipe out the viability of a lot of miners and hash rate will decrease globally. At that point the network will adjust the difficulty until the target block rate is reached with the remaining miners who can afford at that expected payout.
Yes, but that is still subject to the cost of actually doing the processing. It's perfectly possible that it's net-negative for anyone without free power in a certain area.
There can even be load differences when it's just not worth enough that every gamer will bother setting their machine to hash in off hours.
The most recent goalpost shift put the merge in September.
... honestly doesn't sound smart at all. Are they also buying or just overpaying by mining?