Azure Data Factory: Parameterization and Keyvault within another linked service

Question

In Azure Data Factory I have a Key Vault which is used by several other linked services. All of the linked services have been parameterized, except for the Azure Key vault URL within other linked services. See below:

When I save, ADF automatically enters the value for the URL, from the parameter found in the Key Vault linked service.

The team that are setting up our CI/CD pipeline are having an issue, that while the value is changing for the parameter in the Key Vault linked service. It is not changing in the linked services which are using Key Vault. (So for example, while Key Vault itself now has the URL for PROD, Azure SQL still has the Key Vault URL for DEV.)

Do I need to parameterized the Key Vault URL value within all linked services that use it, even though the value already exists in the Key Vault linked service? For me this seems like unnecessary repetition. I have tried to use a global parameter instead, but this doesn't seem to be allowed for linked services.