https://www.nationalmuseum.af.mil/Visit/Museum-Exhibits/Fact-Sheets/Display/Article/197972/mcdonnell-douglas-f-15-streak-eagle/
They have been known to go that high (Check out the F-104 for that* ), but they reach a point where the air is too thin to feed the engines, which is why the operational ceiling is lower. That's where they can fight and maneuver, not just go ballistic and hope the engines restart on the way down.
*
The F-104C Starfighter set a world altitude record of 103,395.5 feet (31,513 meters) on December 14, 1959, while the F-104A previously set a speed record of 1,404.19 mph. This record was achieved by Captain Joe B. Jordan, who also set a time-to-climb record of 15 minutes and 4.92 seconds to reach 30,000 meters (98,424 feet). The F-104 was the first aircraft to hold simultaneous records for speed, altitude, and time-to-climbThe all time altitude record for an air breathing jet goes to the MIG-25 Foxbat at 123,523 feet set in 1977 (the plane was modified from the normal line MiG 25).
Most of those altitude records were set by taking the plane essentially ballistic in flight, past ordinary operating ceilings, for the MiG 25, about 79,000 ft.; for the F-104, about 73,000 ft. Climb rate mattered, as it determined altitude after the engines no longer had sufficient air to operate at capacity, if at all.
Operational (horizontal flight), the record goes to The YF-12A, (SR 71 relative, an interceptor rather than recon aircraft):
1 May 1965: Lockheed YF-12A 60-6936 established five Fédération Aéronautique Internationale (FAI) World Records for Speed: 3,351.507 kilometers per hour (2,070.102 m.p.h.) over a 15/25 Kilometer Straight Course; 2,644.22 kilometers per hour (1,643.04 miles per hour) over a 500 Kilometer Closed Circuit; and 2,718.01 kilometers per hour (1,688.89 miles per hour) over a 1,000 Kilometer Closed Circuit. On the same day, 6936 set an FAI World Record for Altitude in Horizontal Flight of 24,463 meters (80,259 feet).