You are right to question what essential authority HMRC has to require the registration of non-taxable trusts.
HMRC are quite prepared to ignore or stretch the powers conferred on them by law. They have no authority to register estates under the 2017 regs and their other role as taxation authority does not give it to them. They can of course accept as that authority that they will no longer require a Form 41G if a trust is registered.
The authority for registering a non-taxable trust is there but I agree it is scarcely obvious. Regs 42 and 44 apply to all relevant trusts. But Reg 45 is apparently only concerned with taxable trusts. Reg 45(1) obliges HMRC to maintain a register of such trusts but 45(10) (c) requires that register to contain details of non-taxable trusts.
I have no idea why the corresponding obligation to do so was not contained in Reg45ZA itself or by amendment to 45(1). The original 45(10) only applied to taxable trusts. The new version was substituted by the 2020 Regs at the same time as Reg45ZA was itself added. I think the obligation to keep a register of non-taxable trusts is implied by current Reg 45 but it is an unsatisfactory link.
The register can only contain the information in Reg45ZA(3) and (4). The former does include details of an individual (but not any other person) referred to in a letter of wishes as a potential beneficiary. I have corrected what I first said athttps://trustsdiscussionforum.co.uk/t/trs-and-letter-of-wishes/20016/2
Jack Harper