Every time you apply for a card it's a hard pull on your credit. You have also just put all you info into another database that can get hacked. There may be no fees now, but you will likely forget you had this card, terms and conditions change, and all of a sudden you are being charged to keep an inactive card open.
My ex had this happen. Signed up for some card and used her college address. Terms changed and she started getting charged for an inactive account. Not much, but enough for there to be a balance, followed by a late charge, followed by interest. This went on for quite some time. They kept sending bills and notices to an address she no longer resided at. We were notified of the situation when she was served papers by a collections agency and at that point it was thousands of dollars.
[This space for rent]