A team can hedge more easily than a player. Teams can sign multiple pitchers cheap to hedge in case some don't work out. Essentially, that is what Oakland and Tampa have done. Oakland signs Trevor Cahill and Brett Anderson cheaply. Cahill is not great, but on a good enough contract that he is then swapped for Parker. Tampa turns out to have probably made a mistake in signing Wade Davis early, but the Shields signing worked out really well for them. Davis did not stop them from signing Moore dirt cheap.
A player has different incentives. I don't think insurance on a pitching arm is all that easy to get anymore. Most arms have some damage, and certainly you don't want to be turned down by an underwriter and raise a red flag. Beside the injury factor, there is the possibility of not hitting expectations. Call it the Wade Davis / Trevor Cahill factor (or Clay Buchholz / Jon Lester factor). It is pretty tough to turn down millions early unless you have an enormous [sense of confidence]. Getting several million guaranteed early, maybe even before you hit arb, and giving up a year or two of FA for $12 MM per in options is a lot to pay for the possibility of making $18 - 22 MM if you turn into Cole Hamels.