Worse yet, the value that Bitcoin fees have to protect is 2 orders of magnitude higher than for Doge.
The attack target value is not related directly to market cap. It is related to the potential the attacker can double spend.
I believe that number to be more related to the average value in purchasing parity that is transferred in each block.
Let's look at such an attack and how it would be peformed:
- The attacker buys the Bitcoins he wants to steal (and probably mixes them a bit)
- He spends the transactions in a single block, to different merchants and exchanges.
- He begins to mine in secret.
- He waits until the confirmation period at all merchants and exchanges is over and all orders are confirmed. Probably most of the time he'll try to swap the coins for altcoins.
- He takes over the chain and "rewinds" all his transactions.
The merchants and exchanges would all have some kind of maximum value he can deposit. This maximum value, however, depends on purchasing power and not BTC probably. Let's say he tries to spend 100,000 BTC (6 billion USD) on 1000 different platforms, 1 BTC on each platform. This would not be a problem with 60,000 $ per BTC. But it would be probably a problem with 600,000 $ per BTC, because only a few platforms would allow such big deposits. He would then have to try to scam a lot more platforms, which makes the attack more complex.
So I believe there is some relation between market cap and double spend potential but the relation is not linear. It would even be somewhat detectable: blocks with an unnatural spike in transacted BTC could rise the alarms in merchants and exchanges, and make them rise the confirmation requirement. That's why I think the attacker would try to stay inside the normal limits, and thus be bound to the average transaction volume.
Another source of income for the attacker are short sales but this is way more difficult to predict, it is probably more related to market cap, but also related to the number of BTC (and their value in USD/purchasing power) available for lending and the security measures of the trading platforms. Most trading platforms would probably stop trading as a security measure when they detect a long reorg, and thus the attacker may have severe difficulties in re-buying the coins without having to go through some sort of scrunity for the sources of funds.