Kinda bad idea from the way I look at it.
It would be too easy to track exactly how traits are passed down and the exact dominance/recessiveness of them. I know people have their own lists for that, but they are not as absolute as something like this would be. So after you collect a few hundred pedigree and notecards Im sure some savvy programmer could make a program that indexes how traits really are passed down or you can of course do it by hand too and make a spreadsheet.
But I wouldnt mind getting a NC when they reach 120, like a fortune cookie. Only drawback is that no one will menagerie cats for a few weeks and keep them in inventory instead to get their fortune cookie then menagerie