Not all countries have a "weak local currency" currency policy. Some will let the currency freely float against other currencies regardless of what the market does. The only currencies that will have the problem of being too strong are countries that have net exports as their currency will naturally get stronger as they sell products overseas, bring the profits home and buy the local currency.
The problem is what happens when other countries manipulate the foreign currency exchange rate. Do they still follow an off-hands policy or do they intervene in the market?
Most will still follow a hands-off policy. When a currency market is intervened in, the impact is almost always temporary as intervention only slows the appreciation of the currency not reverses it over the long term.