Once a falcon 9 second stage has burnt all its fuel, a crew dragon is left in LEO with very limited delta v budget remaining. To intercept the space station it needs to be launched into a very specific inclination and at a certain time. It's very much unlike a jet that has a thousand km or more of range and freedom to change direction and altitude at will.

Unlike a fighter aircraft or multi role strike aircraft that might need to change directions or mission on the fly, or extend its mission on a spur of the moment decision by refueling from a tanker, the crew dragon mission is planned out meticulously to the tiniest thruster detail in advance.

Not that military missions are not also planned down to the smallest detail, but systems are also designed to work within the needs of a rapidly changing tactical environment based on opposing force actions. Aircraft intended for tactical roles that can be air to air, air to ground strike, radar suppression, etc, need a great deal more flexibility.