I think if you had Tampa's outside the box thinking but with the White Sox roster (young, super talented, charismatic, marketable, etc), then it would be less annoying. It's just that they do what they do in addition to having the most white meat, dull, super bland roster ever (combined with all the other crap they do as already mentioned). They'll never have a franchise player anymore because they'll trade him as soon as he's arb eligible. They'll never have fans because of the location of their stadium. Their style of play is literally the embodiment of what baseball is trying to get rid of. If you ask young non fans about what they find boring about baseball, they'd unknowingly describe the Rays almost perfectly.
You can appreciate that they get so much out of so little, but it's still bad for the game. At least the Moneyball A's had players opposing fans would be able to name. The Rays are just so boring.