Apparently, you are not the only person to notice / comment on this behaviour; see this "tomcat-user" posting:
(Indeed, the similarities between that posting and your Question suggest that there is some connection between yourself and Andry Eng ...)
So clearly, this is "expected" behaviour in some sense.
Whether it is "correct" is a matter of opinion. And it is moot if the Tomcat developers don't agree with your opinion.
And, for what it is worth, posting rhetorical questions here about the "ideal" behaviour is also moot. Apparently, the Tomcat developers either don't hang out in StackOverflow / "tomcat-users" ... or they are not willing to debate the issue.
So what possible solutions do you have?
This linked Q&A explains a workaround - How to process servlet requests during long shutdown
You could open an issue on the Tomcat issue tracker. The snag is that your issue could sit on the list for months or years before it is addressed. Or it could be "dismissed".
However, it doesn't look like anyone has submitted this as an issue in the past.
You could figure out how to modify Tomcat to reject new requests during shutdown. Then submit your (tested) changes as patches.
You could hire someone to do the work for you. For example, take a look at the people / organizations listed here: http://wiki.apache.org/tomcat/SupportAndTraining.