First off, price would not be 6-20 billion dollars. Very possibly over 100 billion dollars. Oh and don't forget all these people are gonna be paying taxes on their ETH sales so add a bunch more billions of ETH needed to sell.
You're talking about suddenly trying to purchase an amount equal to ALL the miners in existence, AND having to compete for these purchases with the existing mining industry which is always expanding, so prices of ASICS would go up. This would take wayyy more money than you suggest, and years to accomplish.
Then you need to add in the cost of finding places to run miners and set up the infrastructure, so add more billions of dollars.
Selling the Ether to get this done would drastically decrease Ethereum's price, meanwhile Bitcoin's price would be unaffected, making Ethereum's long term outlook to other market participants look weaker and weaker as the attackers are selling and setting up this plan over the course of a few years.
Oh by the way, in the several years that it would take to set this all up, the rest of the bitcoin hashrate will have grown so then these attackers will have to spend even more time and money (and selling ETH) to account for that and still be able to pull off the attack.
Finally, the people engaging in the attack would now no longer have a reason to want to do it because now instead of being Ethereum owners they are Bitcoin miners! They sold their Ethereum to mine Bitcoin. They are bitcoiners now, no longer participating in Ethereum. Their economic value is now tied to Bitcoin, no Ethereum. And besides, as stated above, by the time the attack could actually go off, Ethereum's market will have lost a lot of ground to Bitcoin so many of them at that point would probably not want to go back to Ethereum anyway when they are already now participants in a more successful cryptocurrency.
See how your entire idea works against itself. This is the power of Bitcoin and PoW. Bitcoin has global-level security and engaging in a 51% attack is pure folly.
It's not rocket science to find out the Capital Expenditures of Bitcoin miners. Many are publicly traded companies with open reports. I think the authors of the referenced paper, Nuzzi et al., have been able to make a valid estimate.
Yes, it would take some time if the Ethereum stakeholders choose to set up the farms themselves, but it can be be done, even if it will take several months.
This is a bit of a tangent but you mention that Bitcoin's price would be unaffected. Personally I don't foresee that. It seems to me that when knowing that an attack is underway, some Bitcoin investors would already start to get uneasy, and some would sell their bitcoin. And since this will cause the price of Bitcoin to drop, the 51% attack will then only be easier to afford in theory, as the mining rewards would be decreased and some of the honest miners therefore ought to fall off. This could create a feedback loop where, once the attack is looming in the near future, more and more Bitcoin investors will migrate elsewhere, potentially to Ethereum.
And just to put things into perspective, if we assume the lower estimate of around $6B for the attack, then even if only 20% of the Ethereum investors choose to contribute in funding the attack, they will only have to part with money proportional to 5% of their owned Ether in order to afford it.
And while we are on that topic, there seems to be people here who doubt that the Ethereum investors would be able to withdraw even as low as 1% of the total Ether without causing a crash of the whole cryptocurrency. But even though I personally find this proposition kinda far-out, in reality most investors do not just invest in
one thing. The vast majority of Ethereum investors would thus have other kinds of assets as well that they
can trade, and most likely easily more than ~5%. I hope we can soon put this particular sub-discussion behind us.
But if the participating miners simply rewrites the blockchain ledger and steal a lot of bitcoin
What do you mean "steal a lot of bitcoin"? Do you know how the blockchain works?
No amount of mining allows someone to steal bitcoin from other wallets. In a 51% attack the attackers can choose which txs to mine and which not to mine so they would be able to censor the transactions, and they can double spend their own bitcoin, but they can't steal any bitcoin. The only way to steal would be from the double spending, stealing from the merchants they were supposed to be paying. And if a 51% attack is happening, pretty quickly everyone is going to know about it, and it'd be easy enough for bitcoin participants to stop taking payments from known attackers addresses until the attack ends. This is where the transparency of the Bitcoin network comes in handy.
Besides, the entire idea is preposterous for the reasons outlined in my previous comment.
If the attackers rewrite a large part of the ledger, they can keep all the transactions that they want while discarding or replacing all the others. If they thus make sure to trade a lot of bitcoin back and forth in the time before the attack, they can in principle steal vast amounts if they then keep all their incoming transactions but discard and replace all outgoing transaction from their wallets.
This is but one example of the harm they can do. It is widely accepted that a 51% attack would be devastating to Bitcoin. (But we can of course discuss it further if you are not convinced yet.)