If the country's primary goal is to evade sanctions and improve financially instead of espionage or anything similar, they'll probably opt to attack Bitcoin. I'm pretty sure North Korea isn't developing quantum computer though. If not, then I think most countries would just start with deciphering the encrypted communication.
The problem with quantum computers isn't with the kinds of algorithm that we could move towards in the future but the exposed public keys which would be inherently vulnerable even after the network forks to a new algorithm. Do you burn them or do you just leave a few million Bitcoins to be able to be exploited. Sure, quantum computers are expensive and the cost/benefit doesn't add up but as time goes by, these Bitcoins could eventually be a suitable target. You won't know if anything was broken by ECDSA; spending the 50 Bitcoins from the exposed addresses could just very well mean that whoever controls the private keys wanted to spend them.
Okay, so this is probably the only legitimate counter argument that could be presented that's for quantum computers becoming a risk to cryptocurrencies, and I can't really argue that fact except for; By the time quantum computers come available which are capable of breaking the ECDSA, I'd expect us to have a solution via a quantum resistant algorithm already implemented. Of course, this would require a fork, and not everyone would be willing to move or some people aren't going to move. At that point, you'd probably expect that a lot of coins would be available to target, but if we have enough notice, and good enough reasons to fork then I would expect the majority of people would move their coins to the quantum resistant algorithms.
So, this just leaves the coins which have been lost prior, those that didn't want to move, or those that didn't hear about the fork. These are risks, and unfortunately will happen when it comes to it. These coins could be targeted, however if they've been given good enough reason to move, and enough timeframe then they themselves are taking the risk of leaving their coins there. So, they accept the risk of losing them.
That being said, when this does happen the affordability still comes into consideration. If its only high profile companies, and governments that have access to quantum computers capable of breaking ECDSA, then they aren't likely to be interested in coins that have been left. First of all, there's no real motive. The issue is when quantum computers become accessible to your common criminal, those are the ones which would more than likely be interested in targeting these coins, but by the time that happens there will be enough notice, and will allow people to weigh up the pros, and cons.
I don't think in the grand scheme of things, its a major issue. There's multiple factors which have been mentioned above which will delay the threat of quantum computers, which should allow adequate time for planning, and implementing a solution, and having those that having doubts about moving to a different protocol, time to make up their minds.
We could burn them, given enough notice that does seem very extreme though, and I'm not sure that's the best decision. Undoubtedly, any coins that are left that can be exploited, will likely be exploited eventually, and that would likely have an effect on the short term value of Bitcoin.