re: what is the use of the Custom Field option if only the admin can use it from the WP admin panel and the front user cannot add or edit it
Other than the reson I already mentioned. The Custom Field was modelled after the same Custom Fields metabox found on the admin Posts and Pages pages which require more privileges than a subscriber has permissions to access.
Also this is to limit complexity for the user reducing potential confusion as for what that would be used for.
It is an advanced feature in which you and I understand its features and function but this not something a typical user is going to understand.
What would be a better solution for you would to have a custom metabox presenting the user with checkboxes of options where they can choose from a list of predefined options that they can check which would display in their profile.