I don't think this one is as automatic a win for the Rays as it may seem.
1) Shields is a legit top tier pitcher and Davis just had a stud season in relief. That's a big boost to the Royals' pitching staff.
2) The Royals have the money to spend.
3) Royals prospects have a way of crashing and burning. If you look at a modern history of the KC franchise, it would have been a lot better off trading guys like Jeff Granger, Jim Pittsley, Dee Brown, Chris George, Runelvys Hernandez, Kyle Snyder, Jimmy Gobble, Angel Berroa, Colt Griffin, Chris Lubanski and Luke Hochevar before they disintegrated. Myers looks like the real thing, but Odorizzi is no sure thing and Montgomery has been a bust so far. I think there's a general assumption that the Rays can polish turds into diamonds, and they very well may need to with the arms coming over from KC.
And what if Myers isn't awesome? Kind of like how Eric Hosmer and Mike Moustakas haven't been awesome yet. And how it took Alex Gordon five years to figure things out. If Tampa Bay gave up Shields for that, then this deal isn't going to look so good on their end.
On the flipside, the Royals had a fairly poor offense last season. I know the in-house thinking is that the lineup will come around, but you don't get to be Royals-bad having just one flaw.