FLU, I hope you’re kidding… The more I read your posts, the more convinced I am that landlording is not for you. If a fridge is leaking water, you do want to know about it. Water can damage your asset (house)! “Never bug me again” is not the proper strategy (unless they are bugging you about really trivial stuff).
I know, elsewhere you wrote “no problem, I just dock their security deposit.” Water damage, and many other kinds of damage can be costlier than a 2-month rent deposit. More generally, as a landlord, you shouldn’t be fostering an antagonistic relationship with your tenants, especially as long as they pay rent on time and are not complete pigs. One should never befriend a tenant, but that doesn’t mean he’s your adversary.
I do agree with your points about having a simpler fridge; however, if the house is in a nicer neighborhood, it’ll be hard to rent if you don’t have a relatively new fridge with ice maker and water dispenser.
A solution for some landlords is to exclude a fridge from the house, but offer to rent one out to the tenant for, say, $40 a month. If the tenant doesn’t buy his own fridge, then you can buy one cheap from Craigslist. If it breaks down, then just buy another used one.