It’s generally considered bad form to rip the wings off of the orbiter during the ascent stage or all the fairings off of the rocket before the payload makes it to orbit.
Technically most of the rocket is an aircraft. A ballistic aircraft, but it only operates in air nonetheless. First stage drops away before it’s outside the atmosphere on most.
And those SpaceX folks, they’re operating them in air on the way back to the pad.
Really the payloads are the only thing truly designed to only be a “spacecraft”. The booster systems spend most of their time operating as an aircraft, if you really think about it.
Upper stages less than lower.