Kevin: Agree with you, xC000005's suggestion to you was very bizarre!
Here is our experience as to why this issue is very bad. We produce an addin for Outlook and our addin adds both custom named properties and X-headers to messages sent by our users.
Some of our users have complained that with our addin installed, some of their messages sent to other users in the same exchange system get bounced with messages like:
"The message reached the recipient's e-mail system, but delivery was refused. Attempt to resend the message. If it still fails, contact your system administrator. "
We believe it's due to hitting the named property limit on some exchange databases in their system.
So it seems to us that the short answer to your question "Why should we care if the named property quota is full" is that if it is, messages don't get delivered!