Under Settings > Company > Client Options > Required Fields we show normal client fields, and have 2 options for each: Required, and Show.

It is necessary at times to show the field but not allow a client to modify it. Add a new column with a new checkbox at the end called "Read Only", add a Tooltip that says "If checked, the field cannot be modified by the client if it contains any data."

None of the boxes should be checked by default. If a box is checked, and the field contains no data, the client should be able to set it. So, a field can be Required, Shown, and Read Only. The client would be able to set the field during account creation with no trouble, but they would not be able to modify it later if it is Read Only.

Take this use case as an example:
We have a policy where we charge for license transfers. A license holder pays a fee to transfer a license to a new account or another user. However, if the client has only 1 license they often just give the credentials for their account to the buyer and skip the license transfer fee. The new user then immediately updates the name and company on the account. In this case, we would Make First Name, Last Name, Company/Org, and possibly Email "Read Only", which would deter these kinds of transfers, because they would become known when the buyer opens a ticket and requests a change for the information.