Jon Kraus wrote:
What's incorrect about No Joy? It is only two syllables instead of the
seven for Negative Contact and not considered "banter" at all.

Because it's not in the standard phraseology that is designated by the
AIM and the ATC Handbook as conveying the information. "I have
Contact" is more of an issue because it almost sounds like the
proper phraseology for the OPPOSITE meaning.

No Joy tends to get heavily used for many negative responses and
doesn't specifically mean that I have not located the conflicting
traffic.

NEGATIVE CONTACT specifically means that. It doesn't mean anything
else.

Negative Contact is only 5 syllables...

Syllable count is not the definition of communications clarity.
If it were all ATC communications would be abbreviated to single
words and mike clicks (don't get me started).