This has actually been one of my biggest complaints against the Chinese government. Instead of using China’s USD reserves to buy U.S debts or lend to developing countries with dubious capacity to repay, they should allow Chinese citizens to diversify their portfolio. People are more willing to consume when their investments are more diversified and hence more secure.
My worry is that some crooks might "invest" offshore to move their money out of China. This can lead to capital flight, a serious threat.