After you're on the plane, it would probably become apparent that you and your spouse are married, or at least related in some way to each other. If you have some game with your spouse where you pretend to not know each other in public or something, I guess maybe it could ruin that, but otherwise I'm not sure what the harm is.
Anecdotally, I've noticed that they tend to be more senior (so know what's possible / what they can get away with), less busy (so they're less frustrated and frazzled), and tend to deal with much more experienced travelers than a normal gate agent (so, again, they're less frustrated).
Thanks to mergers and lack of DOJ anti-trust enforcement there are now only legacy airlines.
Unless you and your wife are the only married couple on the plane fitting that criteria, it's irrelevant.