I think the answer to your question is that eventually the US Navy will have to reassign all its carriers to the Indo-Pacific.
We've seen this happen in the past when the reigning global navy concentrates its forces when there is a credible challenge to its naval supremacy.
Plus China exporting large 003 carriers is not going to happen. Even Russia struggles to afford a single carrier, never mind any other potential customer.
That would play right into the hands of Chinese long terms strategy. Because China's real vulnerability is in Central Asia and South Xinjiang (Kashmir, Afghanistan direction). These are the lang bridge between China and the Middle East. If the US will eventually put all its naval forces in the Indo-Pacific, it will significantly weaken the US's control and presence over the Middle East, Europe and Africa. And it will legitimize China's naval build up, while also minimize the threat against China's plans in Central Asia, CPEC, and connect to the Middle East through to Europe. Therefore, the US will have to at least destroy and conquer Iran, before she can safely move all her naval forces to the Indo-Pacific.
China has no problem building a lot of powerful warships to counter the US navy. What China has problem with is the fact that China has to be a trading nation (it has a significant demand for raw materials and foreign market at the same time), and trading nations need to maintain a peaceful and non-threatening posture to everyone. This means that any excessive military power (power without clear and legitimate purpose and target) will hurt that image and cast fear and doubt in other small nations contemplating on deepening their trade relations with China.
In fact, by becoming militarily aggressive towards China, the US is actually helping China to put its neighbor at ease. They were afraid that China's war power are aimed at them, now the US steps in, they will be relieved that the US will draw the majority of China' war power towards the US. This would make these country more confident and at ease to trade with China. So it is a bad move by the US. In fact, you could say that every so-called "restabilizing actions” by the USA's show of force in the region, will actually benefit China. What the US actually need is to stay away and make those nations feel "unprotected" and fearful of China's military power. And then, these nations will come crawling to the US, begging for protection and assurance. And China, in order to assure these nations, will need to cap her military development, deployment and expansion.
In fact, I would say that the assurance of safety to these small nations is something the US should intentionally ambiguously deny. The more these small nations are assured of their safety in dealing with China (because they have the US at their back), the more bold and comfortable they will be at enlarging and deepening their trade relations with China. If the US military stayed away, these countries will be more cautious, and they will also more actively solicit US help and involvement.
Just look at Singapore. Before the US's pivot to Asia, Singapore was always very suspicious of China, calling for US intervention and attention to the region. Right after the US actually pivoted to Asia, Singapore start criticizing the US a lot more. This is a typical petty person's mentality.