I don't know the specific rules in the US, but in Europe that would be illegal. You have to carry your license with you (and we don't have credit-card sized ones just yet) and you'll also have some explaining to do if caught flying without a map of some sort.
My license, medical and other required documents are in my wallet, in a zipped pocket in my flight suit. Are you seriously telling me that you keep all this stuff on your kneeboard?!?! And before I get any other helpful suggestions, I also carry a handkerchief in a zipped pocket too. No uncontrolled sneezes here.
The US does not require a chart to be carried - we are a (relatively) nanny-free environment. If it did, I'd use - you may have guessed - a zipped pocket.
As far as practicality is concerned, you also need to have a plan to divert. Suppose somebody else has a landing mishap and blocks the runway for an hour or two. Do you have everything on board for a succesful diversion, or do you have a different plan B?
My god, you're right, I never thought of that. I suppose I'd just have to lawn-dart myself into a primary school. Thank goodness you thought of this and pointed it out.
Alternatively I could just use the other runway. Or, if a KC-135 had crashed or something else that would block the whole field, I guess I could go to one of the other half-dozen airports that I know off by heart and are within even the Pitts' feeble fuel reserves,