They do, in fact all the time.
You just don't hear about it because of stigma.
See this NARCAP (civilian flight safety) report https://www.narcap.org/blog/narcaptr20 for a case where a FedEx flight crew documented an encounter with the commonly reported pulsating orb type anomaly. There is a video.
Observed behavior:
> The UAP/Light came from above and stopped/hovered near FL37, about the same altitude as the aircraft, shone a light on the 767 and briefly approached the aircraft. Then it instantly matched the speed, and heading of the aircraft and maintained a consistent separation.
a. The light descended vertically, stopped abruptly, and shone a light on the 767 causing the crew to believe that there was another airliner on a collision heading with its landing lights on.
b. It changed direction from vertical descent to a sudden stop/hover, to approaching the aircraft briefly, to taking the same heading and speed of the aircraft at about the same altitude and an estimated distance of 1-2k ft.
c. It matched the altitude, speed, and heading of the aircraft, 575mph and at 37,000ft for over 32 minutes.
d. The UAP/Light changed colors and turned away from the aircraft on a perpendicular heading, West, just inside the Mexico/US border.
e. The UAP/light did not have wings or running lights. It was a new and unique observation to the experienced air crew.
> It seems very, very unlikely aliens would have any interest in our military capability
And in fact, apparently they do here too. It's been documented these UAPs have an interest in our nuclear capabilities. There has been many testimonies from people in the military these UAPs buzz around nuclear silos and apparently are able to disable them. See this well researched video for information on Robert Hastings https://youtu.be/l4EXL7jgqns