Except those waters aren't Chinese territory, which is the entire point of doing freedom of navigation cruises....to remind them of that fact
The recent China-Russia operation was also in international waters, and you'll notice it's only a handful of senators making a stink about it to get some publicity, the military was pretty clear that it wasn't a problem. They just shadow it like they always do.
I mean, they don't have to be allowed in international waters, you just need to get all the planet's seafaring countries to dedicate all of their naval resources to a blockade of the US.
The cheaper option is to realize that the USN is generally pretty serious about enforcing freedom of navigation in a way essentially noone else is able to, which is a net positive for the planet. Even when you factor in some of the shady activities and plain old fuckups that they are occasionally involved in.
Frankly I'd be thrilled if China would actually act like the modern global power they clearly want to become, rather than joining Russia in some 1800s imperial LARPing vs the rest of the world.