Field doesn't update values in profile display

I have an INT_FIELD that updates a TEXT_FIELD when in edit profile.

INT_FIELD is visible in profile edit (not profile display)
TEXT_FIELD is visible in profile display (not edit)

My problem is that when I set the TEXT_FIELD as hidden from edit profile although in console I can see it gets the new values from the  INT_FIELD and then I update the profile with the new values, they are not updated in the profile display (TEXT_FIELD holds the old values).
The same applies when I turn the TEXT_FIELD to read only. In edit profile it shows that it is getting the new values from the INT_FIELD but when I click update profile, in profile display I see the old values.

When I turn the TEXT_FIELD as visible in profile edit, then it updates its values.

How can I turn the TEXT_FIELD to hidden but still get the values from INT_FIELD?
$('input[name=TEXT_FIELD]').val() doesn't solve it.
What attr does it get when I hide it only in edit?

You can't save a field that doesn't allow saving. Marking it read only or hiding it with CB Conditional will block the save process. That is working entirely as intended. If you have a field that has no save behavior, but you need some sort of logic in it use a Code Field (CB Code Field) or Query Field (CB Query Field) to have custom PHP or SQL ran for whatever display logic you're needing. You can also use substitutions in a Custom HTML field for purely substitution and HTML solution.

Ok I understand but I am a bit confused because I have a hidden DATE_FIELD that updates with an AA normally (although hidden) in profile edit on onAfterUserUpdate.
So why in this case it works?

CB Auto Actions pushes directly to the database or user object in its Field action. This process does not care about normal field save behavior. That's why that works.