Their job isn't to chase other submarines next to Chinese waters. That is suicidal. Chinese submarines are almost as stealthy as the Virginia class, and they'll have to operate in the middle of Chinese anti-submarine warfare. That is to say, they won't survive long.
Their job is to actually sink the merchant ships. The US can't do that easily with surface combatants, because getting close to a strait means compromising your position, which means risking getting suck by a Chinese hypersonic missile.
There is absolutely a sensible retaliation from China, that's to sink the US fleet in the pacific using ground-based weapons which can't be destroyed.
Hence why submarines are interesting to the US, it's the only way to force a blockade without risking destruction by very powerful Chinese anti-shipping weapons that can't be destroyed with ease.
Also, the entire blockade strategy itself is a risky gambit. China has enough stockpiled as far as oil goes to guarantee 100 days at full consumption without any imports, and before any invasion of Taiwan they would make sure to secure enough overland imports, stockpiles, and domestic production to allow for over a year of oil.
Meanwhile the political costs of blockading the Malacca Straits and co will be devastating to the US. It will be the US's Suez Canal Crisis. China will keep Taiwan anyways.
China is definitely going to break through the first island chain. 4-8 Virginia class submarines are not gonna change anything there. They are not invulnerable superweapons, and if they were the US already was going to use them.
Without air supremacy and given the massive concentration of Chinese anti-submarine assets, operating in the first island chain is a completely suicidal option.
The only possible way for this to happen is if somehow the US manages to get Russia on board with a blockade.