The US has been the naval hegemon and guarantor of global shipping since WW2. It also was WW2 that created this navy and it continues to be its founding raison d’etre. China on the other hand cannot justify a naval buildup other than to pose as an alternative or complementary hegemon. But either way it isn’t as strong a narrative and considering that the US navy is doing a good job keeping trade lanes open (except for around the horn of Africa), there isn’t really a need for a strong navy either. Simply having the right to build one doesn’t justify actually building one in the eyes of China’s neighbours.
As for neighbouring countries being more reliant on Beijings good will, that only goes so far. Nations like India and Vietnam are fiercely independent and territorial issues hamper improving bilateral ties. Many in Vietnam prefer the Americans and quite a few enjoy sticking it to the Chinese.
China itself is terribly vulnerable to trade shock. It desperately needs to maintain secure access to energy and other resources. It has to develop its own shale resources and alternative energies in order to become independent. Doing so will be helpful but won’t secure access to other raw materials.
As for the long range DF21 missile which can hit a US carrier one has to wonder: so what? US carrier groups may at one time be globally vulnerable to an ICBM version of the DF21. But the actual act of destroying a US carrier group is a different thing from having the ability to; it would be an escalation akin to Pearl Harbour and would push the scale of conflict meter squarely into the red. And even if the US navy was ever incapable of policing the world’s trade lanes, how would the collapse of the international trade order benefit China? It’s not like they have anywhere near the naval capacity to secure trade and neither would anyone except Robert Mugabe welcome them as liberators.
China can’t challenge the US without a vast navy but can’t build a navy anywhere near that size without challenging the US. And China can’t solve that problem.