one way to do this with the GUI is to create a DB rule for Person and for the update select "Related Item" and then select "Telephone" from the list. When you then select Field you will then have the option to update the primary number. You can set the update to make empty the field by using a function.
To triger the DB rule you would add a boolean field - check box to the person record and set to a default value of unchecked. Trigger the DB rule to fire when this check box is ticked. Either do an update all on person records to set the value to checked for the boolean field or run a UI rule to do the same. This doesn't however remove any secondary phome numbers.
Unfortunately, this solution doesn't work. First of all, it can't remove object "phone number". The rule can update (make empty) field "number" and modify it's type. But the number cannot be empty because it is required and this is not customizable.