Because the register is the ledger, there is no separate register to reconcile against the fund's accounts, and the dealing engine, the fee calculation and the investor's view all read from the same record. The chain is typically private and permissioned, with the administrator controlling who can hold units.
This is distinct from issuing tradable tokens to investors. Units on a tokenised register can be non-transferable and custodial, exactly like shares in a traditional register, while still gaining the automation benefits.