A huge BTC market cap could a have small number of only low value transactions requiring very little network security. Similarly, a small BTC market cap could have a large number of high value transactions requiring a lot of network security. So I still don't think the network security needs have a lot to do with BTC price, but I do see your point that the network security needs have a lot with how enticing it would be to steal by reverse&respend. I am now thinking that the network security needs are most closely related to the value of transactions being performed. Anyway, I still don't see how how the supply of computational power (i.e. BTC price) always happens to exactly balance out the demand for computational power (i.e. value of transactions).
This is like asking if your safe could have a weaker lock. Probably yes, but lets not.
I see your point about more security being good, but another way of looking at things is to question whether it makes sense to pay $4,000,000 per year for an ultra secure safe to store $10,000,000. In this example it might make sense to “have a weaker lock”.
If you view the Bitcoins being awarded to miners as a network security costs, you can calculate the percent of the Bitcoin market cap that goes to pay for network security. For example, currently bitcoins are being awarded to miners at a rate of 10,500,000 bitcoins for the first four years (i.e. 2,625,000 per year) and the current total number of bitcoins is 6,615,750. This seems like a huge portion of the market cap going towards network security and so I wonder if it is really necessary. It just seems like a lot to spend 2,625,000 BTC in a year on network security especially since I don't believe there has been one report of a reverse&respend.
A lot of people want to look at two factors and try to make a decision about which one is first, and which one is second. Things are rarely that simple and direct.
Bitcoins are valuable because the network is secure, and the network is secure because bitcoins are valuable (that is, because there is an incentive to increase security). The two chase each other endlessly and cause each other. You can't pick one and say that it is the cause and the other is the effect.
If you are thinking in terms of the safe analogy (which isn't really very good), remember that everyone in the world is free to use this safe. Having it be far more secure than it needs to be will invite more people to use it, which makes the safe itself more valuable, which makes the safe more secure, which invites more people to use it...
And since the network is distributed, no one person gets to decide how much security is appropriate. If you think that $4 million per year is too expensive to store $10 million, you are wrong, because the rest of the planet has voted, and the consensus is that the cost is exactly right. (Yes, I know, made up numbers. Think of them as references to the current cost and current value, whatever they happen to be at any given moment.)
That is exactly what difficulty is, a worldwide consensus about how much effort we are collectively willing to spend to protect what we have.