The F-16 in fact has a relatively large recline (compared to other fighters). From the main F-16 Wikipedia

The F-16's ACES II zero/zero ejection seat is reclined at an unusual tilt-back angle of 30°; most fighters have a tilted seat at 13–15°. The tilted seat can accommodate taller pilots and increases G-force tolerance; however it has been associated with reports of neck ache, possibly caused by incorrect head-rest usage. Subsequent U.S. fighters have adopted more modest tilt-back angles of 20°. Albano, J. J. and J. B. Stanford. "Prevention of Minor Neck Injuries in F-16 Pilots". Aviation, Space and Environmental Medicine Issue 69, 1998, pp. 1193–1199.

From this archived DTIC Article from 1962 it appears to confirm a lot of what the other answers said. From the summary page:

The prone position of the pilot in high-speed airplanes has certain advantages (higher g-tolerance of the pilot, reduction of drag due to decrease of frontal area, improved instrument visibility) and drawbacks (narrowing of field of vision, decrease of visual acuity, aggravation of claustrophobic tendencies, discomfort encountered in this abnormal position).

Spacecraft routinely have their pilots in the prone position but their main objective is a fairly narrow scope compared to a fighter pilot. It seems the wrap-up answer is that the prone position is useful in the context of the specific mission of a given platform but for military aircraft it doesn't seem to offer an advantage.

The F-16 in fact has a relatively large recline (compared to other fighters). From the main F-16 Wikipedia

The F-16's ACES II zero/zero ejection seat is reclined at an unusual tilt-back angle of 30°; most fighters have a tilted seat at 13–15°. The tilted seat can accommodate taller pilots and increases G-force tolerance; however it has been associated with reports of neck ache, possibly caused by incorrect head-rest usage. Subsequent U.S. fighters have adopted more modest tilt-back angles of 20°. Albano, J. J. and J. B. Stanford. "Prevention of Minor Neck Injuries in F-16 Pilots". Aviation, Space and Environmental Medicine Issue 69, 1998, pp. 1193–1199.

From this archived DTIC Article from 1962 it appears to confirm a lot of what the other answers said. As noted in the comments this in regards to the prone position and not a reclined position. From the summary page:

The prone position of the pilot in high-speed airplanes has certain advantages (higher g-tolerance of the pilot, reduction of drag due to decrease of frontal area, improved instrument visibility) and drawbacks (narrowing of field of vision, decrease of visual acuity, aggravation of claustrophobic tendencies, discomfort encountered in this abnormal position).

Spacecraft routinely have their pilots in the reclined position but their main objective is a fairly narrow scope compared to a fighter pilot. It seems the wrap-up answer is that other positions are useful in the context of the specific mission of a given platform but for military aircraft it doesn't seem to offer an advantage.