Currently registration info is always added to the order view due to commerce_registration_entity_view_alter().
However often it is not needed to show this info. It would be great to make this optional via (global and per product) settings.
Even better would be to not use this alter hook, but provide a pseudo field which then per view mode of the order can be set to visible or invisible.
In our case we send html mails of orders, and the table with registration data is full of links we don't want to see, and hiding it altogether is even preferable..
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