[samus]

China would have open access to the oceans even without controlling Taiwan. The same rules that deny China territorial rights to the South China Sea also grant it access to the oceans. The Nine Dash line is about territory. China wants the South China Sea to be considered its territorial waters where it can make stronger demands about who passes through and what they could do there. It's not the only country trying to do something like that, but international law generally only recognizes the sea up to 12 miles out to be territorial waters.

The Mandate of Heaven is rather more like a justification of de-facto rule and claiming to have lost it is an argument against a failing dynasty. The dynasty managing to unite China would declare it, and as it eventually collapses, rebels would declare it to be forfeit. There would be messy civil war, one of the warring groups would dominate all the others, and the cycle starts anew.

[sandspar]

The Taiwan Strait is extremely efficient for shipping routes. The sea and wind to the East of Taiwan are treacherous. Going the long way round would be very difficult and greatly increase shipping costs for a substantial portion of the world's goods.

[samus]

This is not an issue at all because the current rules permit peaceful passage through territorial waters. That broadly means no lingering, no spying, and going straight to the intended destination. Access can be denied for security reasons of course.

This is totally fine for commercial traffic. Since China has a huge export market, it is also not interested in raising shipping costs.