So that, semi-worst case scenario, if they get stranded on the ISS their air, food and water last much longer. Wouldn’t that matter a lot more than accomplishing a full 7-crew mission since this is essential a ‘proof of concept’ flight anyway?
Assuming that for something like the space shuttle (it’s a BIG ship), 7 people don’t weigh significantly more than 0 people (the computer flying), then it costs less to send up a full 7-crew mission and get all the stuff done that they’re going up there to do than to just send up the shuttle on autopilot to drop off some groceries at the ISS. With NASA, money is a big issue (imagine what they spend on gas!)
The assumption I’m running with here is that supplies won’t weight significantly less for a smaller crew, since the basis of your argument is making the supplies last longer. Any mission-specific equipment for the other 5 crewmembers (ie: everyone but the Pilot and Commander) would get left behind too, but of course, that’s still a lot of money to just carry supplies. We can just send up a regular rocket for that without hauling out the shuttle.
I don’t see the advantage to NASA. If they are worried enough about the shuttle to not be willing to send a full crew-they wouldn’t send it at all. The goal (worthy or not) is to get the shuttle flying. sending a smaller crew doesn’t enhance that, in fact it delays that since the goal is to get the shuttle and it’s entire complement flying. A smaller crew isn’t going to be rescued any faster and there is enough supplies on the station to keep everyone going until another shuttle could launch.
Even if that were an issue, it’s easy enough to send more supplies on unmanned rockets.
Because this mission isn’t just a test mission, it’s also to perform some much needed repair and resupply of the ISS. NASA needed a full crew on the shuttle to get everything done that needed to get done on the ISS.