This mechanism is distinct in that it's not initiated by the LSP to assist the user by covering on-chain fees but rather starts with the client offering a PTLC within the in-factory setup. A crucial aspect of this procedure is that clients have the autonomy to decide against initiating an assisted exit during periods of high transaction fees, which inherently provides no incentive for the LSP to force clients out during such times.

The advantage for the LSP in facilitating an assisted exit lies in the early recovery of in-factory funds. If all clients opt for assisted exits, including transitions from one factory to another, the LSP gains immediate access to funds directly from the funding outpoint without waiting for the timeout period to end. This contrasts sharply with the scenario where the LSP has to unilaterally exit clients, involving extra steps and potential costs during high-fee periods. Therefore, an assisted exit strategy is favored as it requires less block space for the LSP to reclaim its funds. The significance of the client’s private key comes into play here; by safely transferring it to the LSP in exchange for their funds, it allows for a more efficient closure of the construction through a simple transaction without revealing specific script details.

Furthermore, even if some clients do not participate in an assisted exit due to various reasons, like hardware loss, the preference for the LSP remains with assisted exits from other clients. This is because each node within the construction is part of a complex branch structure, and once a subset of clients performing assisted exits is achieved, the LSP can recover the remaining funds from those outputs using the "everyone signs" branch. This method is more cost-effective than preemptively ejecting non-responsive clients, holding out hope for their eventual online return and participation in an assisted exit. This approach underscores the value of private key transfer in optimizing the process for both the LSP and the participating clients, highlighting its efficiency and practical benefits in the broader context of digital asset management and liquidity provision.