I do find it curious that the launch and flight is planned (constricted?) to the point that there is literally no window, while watching the live stream it became pretty apparent that it's go at go time down to the second or not at all.
I wonder if this is more operational choice or if it's strictly a matter of physics and capabilities? Does the spacecraft and mission have the ability to calculate alternate burns and what not to still make a proper rendezvous if the launch happens ten minutes later (as alluded to on the stream, the weather probably would've allowed for given another ten or 15 minutes)? Or is it simply not an option within the spacecrafts abilities? I'm obviously no rocket scientist or judge, just a legitimate curiosity.
Not so much a matter of fuel, as it is of orbital mechanics and safety.
Catching up to something in orbit means you have to go faster than it. Going faster raises your orbit. So now you're above it. To match its elevation and its position in orbit, you'll be burning a lot of fuel.
Falcon's 2nd stage has enough fuel to deliver a cargo like Dragon all the way to a GTO orbit, way beyond LEO. But it's a big engine and using it at even minimum thrust it can put out throws a lot of G's at those humans inside the capsule. So the ideal solution is to use the hypergolic fuel in the Dragon for orbital maneuvering (the OMS engines on Dragon are called Dracos), and only have 2nd stage perform the orbital insertion from the point of booster MECO and final approximate orbital height/speed. That's only a couple of minutes of burn time.
The second stage will be deorbited for this mission probably at least half full of fuel. If the 2nd stage did perform OMS catch-up, it would also have to perform OMS de-acceleration. That would be hours later, and keep in mind that Falcon 9 uses superchilled fuels. These fuels get warmed in space, or cooled, depending on sun exposure. The RP-1 can gel up on the night side, or get too warm on the sunny side. Reliability of engine output goes down from ideal, and you're talking about trying to account for hundreds of meters per second of velocity difference between Dragon and ISS during rendezvous. I think Dragon's full hypergolic load only provides about 400m/s delta-V. Using that to slow down a capsule that was accelerated at the ISS by a 2nd stage is not an ideal situation.
