I really like this idea and finally we are in a stage where we can reasonably support it. There were many ways how to implement this and after careful consideration I have concluded that the best way would be in form a new keyword: Forbidden. I expect this keyword to be added in the Christmas update.
If a card has this keyword it can't be added to the deck during deck construction (including deck import from file). Drawing cards via card effect will ignore cards with Forbidden keyword by default so they won't be summoned by cards like
Messenger. Of course, we are able to have specific cards summon cards with Forbidden keyword by card effect. Additionally, cards with Forbidden keyword can be added to deck during gameplay via card effect as well. This opens up completely new long term strategies that involve upgrading your deck during gameplay.
We could add Forbidden keyword to cards like Searing fire and Purified ashes since both are summoned by card/keyword effect. We can rebalance cards that summon from list of cards by adding Forbidden keyword to some cards on the list. Also, we could add new cards that provide alternative win conditions, like having 15 Forbidden cards in your deck.
Fithz has provided lot of card concepts related to this keyword, so I'll certainly have a look at them.
Feedback is appreciated.