Customer welcome to Just Answer!.
Your wife is right... the 20 incher-ers do look great, but carry a few downsides...
You guessed there might be a slight decrease in mileage and it's probably going to be true. Wider tires that offer a greater treadpatch on the road surface will give the truck better dry-road traction but the friction it coincidentally creates will cost you a little bit in the MPG department. Keep 'em inflated to at least 35 psi to minimize hysteresis and to get the most miles out of them.
Tires can cost substantially more in the 20" size as compared to plain-jane units. You might want to check into replacement cost compared to the smaller size.
Snow or off-road traction will likely be inferior to the 17" tires in most cases. A wider tread patch spreads vehicle weight, preventing good compaction of snow or penetration to firmer mud in the case of 4-wheeling. The tread design on the 20" tires typically is much more car tread-like, with less depth or distance between tread blocks.
They look so good other people will want them, too! You'll need locking lug nuts without a doubt.
Your insurance may or may not cover the new wheels in the event of a curb shot or theft if the company isn't made aware of the parts swap. The original VIN will indicate steel 17" wheels and tires and they may balk at the cost of the larger units (substantially more). I'm sure it can be added into the policy, but will likely carry added cost.
There's a chance the base suspension may not be up to the larger and heavier tire/ wheel combination. It will drive fine, but certain road conditions such as bumps/ potholes/ washboard may be handled better with the exact springs and shocks specified for use with these wheels. I don't know for a fact that this is true or whether you'd notice the difference... but it might be.
If you decide to go with the bigger wheels, it's all good. Nothing good comes without a price (lol)! One thing that the dealer does need to do is to recalibrate the ABS to accept the new tire size. Otherwise your speedometer will be off by a bit, as well as the odometer readings.
Write back if you have any questions.
Congratulations on your new Ram!