It actually depends on how the cost of securing a PoW network scales with the market cap, if it is linear and above 1% Proof of Work is not sustainable but if it increases less than linear the inflation needed to secure the network will decrease will decrease when the orice of the coin increases.
There are two hard laws in PoW:
1) the security of PoW is exactly equal to the waste
2) the waste of PoW is nearly equal to how much miners gain, which is the cost of the system (inflation cost, and transaction fee cost).
The threat model is twofold:
1) economically
2) strategically
The economical threat model is that of double spending, but is ridiculous. Indeed, if ever you succeed in double spending, you will KILL THE SYSTEM, and then your holdings aren't worth anything in any case. So the danger of double-spending is largely overrated. Nobody is going to double spend, simply because if someone is going to double spend, and it works, then the confidence and belief in the system is dead, which means that the coins you took back are worthless now (there may be a window of opportunity to sell them before people realize and the market crashes, though).
--> there is almost no necessity of security against double spending, because the stake holders that COULD double-spend, would destroy the value of their stake.
The true threat model of a crypto is strategically: where you want to destroy the system's confidence, not because you want to obtain value INSIDE the system but because of the system's failure. That threat is worth a certain amount of value to the attacker and the system should be secured such that the cost to the attacker is larger than his incentive is worth.
In fact, this threat incentive is most probably more than linearly related with market cap. It can be "outside economical", mainly through shorting the asset of the system ; or it can be "political/strategical", like promoting a rival system, or purely geo-political reasons.
It is clear that these are "threshold threats". Below a certain market cap, you won't trigger these threats ; above it, you will have to face a huge incentive to break the system. You can even combine both: you can finance your political threat by shorting the system.
Killing a 20 billion market cap thing is most probably not interesting for powerful agencies. Killing a 2 trillion system is. If you need to spend 20 billion on killing a 2 trillion system, that's costly ; but if you can finance that by shorting, you can even get both some financial benefice AND reaching your political goal of blowing up the system.
--> the higher the market cap of a PoW coin, the higher the market cap percentage you have to waste on PoW to protect it. Right at this moment, bitcoin is OVER PROTECTED with its 2% waste cost of market cap per year. Do this times 100, and it is vastly under protected and will be killed if you keep just 2% of waste per year.