The real obstacle is not thrust. The real failure mode is the human body. Strap a person to rocket-like vertical acceleration and the first limit is g-force tolerance, not engine power, because sustained axial loads above about five or six g will pull blood from the brain, trigger g-induced loss of consciousness, and turn any heroic pose into a limp mannequin.
The harsher truth is that flying upright is the worst possible posture. In vertical climb, the acceleration vector runs straight from head to toe, so hydrostatic pressure gradients in blood columns stack up, retinal perfusion drops, and the cardiovascular system cannot compensate fast enough, which is why real high-performance aircraft use reclined seats, g-suits, and carefully profiled g-onset rates to stretch tolerance by precious seconds.
Even if consciousness survived, stability would not. A human-sized body is a terrible airframe: high drag, low inherent static stability, and constantly shifting center of mass as arms or legs move, so any vertical ascent at transonic or supersonic speed would encounter shock waves, buffeting, and asymmetric pressure fields that would twist joints, rip at the neck, and demand continuous closed-loop control far beyond what the vestibular system and proprioception can process.
Thermal and respiratory loads finish the argument. High dynamic pressure drives air into the airway, shreds laminar inhalation, and forces irregular breathing, while convective heating at even modest Mach numbers can burn unprotected skin and eyes, so real aerospace systems wrap the pilot in pressure suits, helmets, and controlled cabins, acknowledging that unaided flesh is the weakest link in any vertical dash to the sky.