How many of them have won a World Series this century? There's only one, so yeah, they aren't being competently run. The current practices of small and mid market teams ARE NOT WORKING. It is near impossible for these teams to win it all with the strategies that are being and have been used, and equally impossible for them to be consistently competitive. If the league has completely crapped it's pants and salary caps and floors are not possible, the Twins need to stop being followers and try brand new strategies. Blasphemy, I know, we like to be reactionary not revolutionary here in the Upper Midwest.
Personally the practice I think they should first try, is to NEVER blow their precious budget on middle of the road free agents unless there are no internal options. Spend all your money on a handful of high quality players and then use your optionable and low cost players for the rest. Keep your 26-man roster as flexible as possible and leave yourself nearly endless possibilities through out the season. Only take the risk of paying a couple of high upside players locking up the roster, not a dozen low upside players you can only part with by burning money.
If that doesn't work, try something else. If they don't like that idea, try something else, maybe off the field. Like forcing the owners of the top revenue teams, which is the minority, to 100% share revenue. Just stop doing what other teams are doing that also aren't working.