I understand that, and maybe you're right. If the US is not going to send an aircraft carrier then maybe it is them that look humiliated.
But in just a few days!
I don't think any laws or rules or norms come into it at this point - not that the US has any continuity of its own in that regard anyway.
What I mean is the international legality of the area means that only an overwhelming show of force would have a positive polticial statement.
As an example, if China sent the Liaoning CSG to international waters outside Hawaii, the US would not be humiliated because it can just send many more ships to surround it. Whereas if say a few years down the line, there are many more PLA CSGs and they send 4 with US being unable to muster anything close in the region to meet them, it would look bad for America.
Just one CV isn't enough in any case to be such an example of overwhelming force. In that case, it is smarter to send 1 or 2 escorts rather than the CV itself, because it looks better if the escorts are surrounded compared to if the Reagan itself gets surrounded.