Of course they don’t have insurance in Woodruff, it doesn’t make any financial sense for the team.
Same idea with an insurer. It would e like writing a policy for a motorist with a history of crashes, why would any company write a policy for a pitcher who already has significant injury history, it would not be a likely money making situation.
Maybe if a player has a 250+ million dollar guarantee they could be insured, as you mention, for very specific outcomes: career ending injury, injury resulting in multi-season disability,