But when bitcoin prices are high, there is an increased risk that someone could launch a 51% attack and start double-spending bitcoins. Keeping the level of competition high does protect the network to some extent. But really it only has to be expensive enough to be unprofitable to launch an attack. Pushing difficulty right up to the point of any mining being unprofitable is a waste.
People tend to think of the rewards as set in stone, but they're completely arbitrary (they just have to be agreed-upon by participants). For example, there's no need for them to taper off over time, we could keep them constant.
It's just a question of what you can get consensus for. The geometrically-decreasing rewards of Bitcoin are probably not optimal, but without centralized control there has to be some kind of pre-determined issue rate.
We could just as easily agree to halve them right now (which would probably reduce electricity utilization as well as network security, as miners go offline). And that's essentially what Ethereum is planning to do - a major decrease in block rewards in the near future, so that they can create deflation (dumb as hell, but that's what happens when you let a 17-year-old run an economy, he has big holdings of Eth and just wants to see the number go up).
https://www.wolframalpha.com/input/?i=n%5E2+%2F+(2%5En)+from...
That's where we are now, and it means the reward will be large enough to drive bad behavior at least until the next halving (probably two years from now http://www.bitcoinblockhalf.com/ ).
By that logic all of human sports and entertainment is completely wasted effort/power.
It is the hashing power of the mining which secures the bitcoin. It's nigh impossible to steal / double spend, and this is pretty revolutionary IMO.
That said, proof-of-stake and other options exist that might also provide adequate security while posing a smaller cost to the network.