That's true. But it seems I wouldn't be able to use any benefits of the card (charge dispute, claims, etc), because of the eyes...
How many times you were shut down by Chase? IIRC you were the only one who was able to reopen a card in less than 18 months after initial shut down. Then it was shutdown again. Then you were able to open another card...
As for the benefits of the cards, well, consider that you have been able to get sign up bonuses again after initial shutdown versus many others couldn't...
Or if you feel that is not enough, then just tell Chase to go hell and you put the spend elsewhere.