Is giving them your wife's phone simply to discourage them from calling for non-emergency situations? Because in an emergency I highly doubt it would prevent my employer from getting in contact.

I do agree about unplugging, but I've never had a vacation ruined by having a work-related text or call steal my attention for 5 minutes. If me being reachable (not necessarily _available_) puts my employer at ease then it makes it easier for me to take the vacations I want to take because they're more likely to be flexible with my schedule during busy times.