Doesn't the league still reimburse like 80% if they apply going that route assuming he's hurt for the necessary time? Also, why wouldn't they insure the contract? That makes no sense.
The league itself doesn't reimburse anything. The NHL has a league-wide injury insurance group policy with a single insurer. It may have been tweaked since the last news of it was made public, at that time it worked this way:
Every team is required to pay an insurance premium based on their 5 largest contracts. The report didn't clarify how "largest" is defined. It likely goes by how much total salary is remaining on the contract, rather then what the annual average is, since the insurance policy would cover future seasons if a player is injured over a multiple season period.
Each team can then choose how to spread their insurance coverage among 5 to 7 players. Presumably either insuring 5 players 100%, or 6-7 players with differing % amounts.
The insurance premiums and contracts are calculated at the start of each season. Though if a player remains injured from a prior season that insurance policy would continue to pay out. The insurer can also proactively decline to insure a player against a recurrence of a prior injury, such notifications also due annually at the time of premium assessment. For example, Sidney Crosby's contract is insured, but it might not be insured against another concussion.
Teams can purchase additional insurance, though there have been many reports it is prohibitively expensive and rare that teams do so. Lastly, the insurance only kicks in after the player has missed 41+ games. So even if for example Nate Thompson's contract were insured, the Ducks wouldn't see any relief until January.
The TLDR summary: Unless a player is among the 5-7 largest contracts on their team it's highly unlikely the contract is insured against injury.