Was looking at CapFriendly LTIR FAQ.
I think this part here explains why they need to be as close as possible to the cap when the season starts:
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When a team goes into LTIR, their effective salary cap, or upper limit, is changed. This adjusted upper limit is calculated as a function of the teams cap space and the player’s cap hit. This value is the “accruable cap space limit” (ACSL), and is the first value calculated. Second are the salary and performance bonus relief pools that are later explained below.
The accruable cap space limit is the teams new upper limit excluding their LTIR relief pools. If the team operates below the ACSL, they begin to accrue cap space. A team can operate up to the ACSL without using their LTIR relief pools, once they operate above the ACSL, they begin to use their LTIR relief pools. In the majority of cases, a team using LTIR will be using their relief pools. Only in uncommon circumstances does a team operate below their ACSL.
The ACSL is only calculated when a team first enters LTIR, if a player is placed on LTIR while another player is already on LTIR, the ACSL is not recalculated. In the event that a team stops using LTIR, their ACSL resets to the default upper limit of the active season, upon reentering LTIR, the ACSL is again recalculated.
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When the season starts (and Leafs need to put players on LTIR, they want the ACSL to be set using as much of the LTIR as possible, because if they waited for Dermott or Hyman to come back the ACSL would be lower.
Another important note is that the Leafs this season will never have a point where they are using no LTIR, so they ACSL will never be recalculated.