The risk, of course, is that you'll seem rude and high-handed asking interviewer-style questions yourself. If you have the upper hand (the job market is hot and they need you more than you need them), that's fine, otherwise not so good.
I love the table-turning style of these questions; but the fact is, they can always answer "No, we can't think of any such examples. Are you going to walk away from the job?"
That is to say, hiring is usually a buyer's market.
In the US, in the tech industry, right now? That's not even close to true.
An aside, I say the above now, but damn, I wish I'd had understood it 10 years ago.
This will help you determine if projects are mismanaged, how stable their prod environment is...etc
Obviously, it's up to management if they want this to be a part of the interview.