Bear with me ... This would be an optional game setting.

Card Refill:
1. Individual, at end of scene (default)
2. Collective, when everyone runs out.

It serves 2 purposes.

1: It ensures absolutely every one gets to play their cards. If you have primarily only 1 or 2 challenges per scene, the same few players, if they're quicker off the mark, can complete those challenges and thus take control of the story more often than other players, players who may not have as regular access to the internet.

With this system, limelight-hogging players run out of cards quickly, and then they're forced to take a back seat to the action until the other players have had a turn too.

2: It also allows for a feeling of tension in cooperative, (as opposed to competitive) teams as the game progresses because now you're down to just 1 or 2 of your 5 players, and the groups success is riding on their efforts. Everyone's silently (or loudly) cheering them on, and hoping they have the cards needed for whatever us narrators throw at them next.

As I said, I would definitely suggest this only as an option in the game settings, not a replacement cardfill mechanic.