There are several solutions that could improve the experience of taking a transit card out of a wallet, swiping it, and passing through a turnstile. Here are some of my initial thoughts; of course, more research and testing is required to come to the best solution.

Exterior pocket outside billfold
This allows frequently used cards to be located and removed more easily. In most cases, this would still require the rider to use two hands.

Card Slider
One solution is to create a drop down slot in the wallet. For the NYC MetroCard format, the rider could slide the magnetic portion of the card down and swipe the card with it still physically connected to the wallet. The card would be held in by a clip that moves up and down with the card. This could be performed with one hand and in one motion. Here is a sketch of what this might look like:

Card Clapper
For transit systems where the card must be fully inserted into the turnstile (i.e. San Francisco), a wallet could have a flap attached to the exterior portion, allowing the user to slide the card out, have it ingested by the machine, and then clasp the wallet again when the card exits the machine. This could be performed with one hand and in one motion. Here is a sketch of what this might look like:

Would these things work? I’m not sure, but it is worth a try. The point is that the little problems with the little things in life add up to big problems overall in lost time, frustration, and inefficiency. Why not tackle the little things one at a time to create big overall improvements?