As far as I know, all tips are automatically billed to your room. Concierge or not.
That is correct. Some tips are "suggested," some are mandatory, and some are completely at your discretion, but they all will be automatically billed to your room to be payed at the end of the cruise.
First, your room will be billed for a suggested tip amount for the room steward, the server, the assistant server, and the head server. You are able to stop by guest services (or tell your concierge host) if you want to change any of the automatically billed amounts.
Also, there are other tips onboard. You are required (it's not optional) to tip the spa workers if you use them, for example. A small tip is added to all bar/coffee bar drinks, and you can increase that (but not decrease it) by noting on the receipt you sign. If you dine at Palo or Remy you can add a tip to the bill. You can specify a tip to room service when you get the delivery on the receipt you sign. But, you pay none of these on the spot, they are all automatically billed to your room.
Some people choose to tip sometimes in cash (for example, in addition to the suggested amount for your server give them some cash, or just give cash to room service). You don't have to, since you can choose to have them all billed to your room (just filled out any receipts and it will be automatically billed).
It is not inconvenient for the cast members (crew) to receive a cash tip, they simply turn it in to the purser's office in the crew quarters and it is credited to their paycheck. Simple for them, so if it is preferable for you go ahead, but really your entire cruise onboard can be cashless.