It matters a lot who does the burning/lockup (or more generally exercises control over the monetary supply).
If the burning/lockup is up to the discretion and efforts of an "Active Participant (“a promoter, sponsor, or other third party (or affiliated group of third parties)” which thereby “provides essential managerial efforts that affect the success of the enterprise”, then this is evidence in favor of securities status.
Conversely, my understanding is that if the burning/deferral is done programmatically by consensus rules, or left to market forces and decentralized control by a loose set of unaffiliated parties (e.g., miners) then it does not support the “Reliance on the Efforts of Others” test.
I conjecture (by the spirit of things) that a legal Trust, disbursing funds by strict and simple instructions and not affiliated with other “Active Participants”, would not provide significance evidence for the “Reliance on the Efforts of Others” test. It ought to be considered just part of the legal plumbing that defines and tracks the asset (which is necessary for any traded asset), akin to the technicians maintaining the token issuance machines in an arcade.
For further context, see the SEC’s framework, and in particular the 1. Reliance on the Effort of Others section and this paragraph there:
An AP creates or supports a market for,[17] or the price of, the digital asset. This can include, for example, an AP that: (1) controls the creation and issuance of the digital asset; or (2) takes other actions to support a market price of the digital asset, such as by limiting supply or ensuring scarcity, through, for example, buybacks, “burning,” or other activities.