If a Big Player decided to undermine bitcoins then they could do so very easily. All they'd have to do is throw enough resources at it to capture the majority of the mining capability and they'd be able to sit on whatever they mine. This would be likely to temporarily push up the value of existing coins, thereby making it much more difficult for any new adopters to jump in.
If the value of existing coins goes up, then people don't need as many of them. So it doesn't matter that they're more difficult to get. It cancels out.
So, by extension, it's practical for the bitcoin economy to continue as it is now, with no more coins being created or introduced than are currently in circulation?
Then when the number of people using bitcoins contracts and the number of services accepting them in payment shrinks (both of which I think would be likely in this scenario) the value of each coin would decrease as the existing supply outpaced the demand.
Then, when the value drops, people can get as many bitcoins as they need. So if you assume the problem occurs, it will solve itself. This tends to suggest the problem won't actually happen.
If they push up the price of bitcoins, people will need fewer of them. If they make bitcoins expensive and thereby discourage people, the reduced demand will lower the price, ending the discouragement.
I think there's a 'perceived value' thing to be addressed. I think that people are unlikey to be drawn in if the price of a single coin is excessively high (in fiat terms).
And don't forget the 51% thing. That's potentially a very big issue. If someone could control the block chain, even partialy, then the intergity of the entire system would be compromised.
That's true, but that's a different issue from them mining. At worst, they could significantly increase the time it would take before you could be assured a bitcoin transaction wasn't going to be reversed.
Yes, I agree that it's unrelated to mining, but it's a very real possibilty if someone decides to throw enough power at it.
Unless I'm misunderstanding things (which is quite possible) then it seems to me that it's also a much much bigger issue than the time it takes to confirm a transaction. Doesn't control of the block chain enable the controller to reverse every transaction (or at least a significant proprotion of them), and also create fraudulent transcations?