Why don't fighter jets take off vertically?
They can climb vertically, but this works best if they are several tons below their maximum take-off mass. Fighter jet engines need a lot of fuel, and at the beginning of the flight the aircraft will be too heavy for vertical climb. Also, the landing gear would need to be rearranged if the plane is to take off from any airport.

Even a thrust/weight ratio slightly above 1 at maximum take-off mass will not be enough, because the aircraft needs some airspeed for its control surfaces to become effective. If no thrust vectoring is installed, the aircraft will be uncontrollable in its initial ascent. The Harrier VTOL jet uses bleed air which is ducted to nozzles at the extreme ends of fuselage and wing for low-speed attitude control.

It is conceivable that the fighter will hang vertically on a wall, with its wheels locked in clutches which will release it when the needed thrust is reached. With thrust vector control the aircraft could be controlled over the full trajectory until it transits to horizontal flight, and could even land vertically. But this would need specially prepared airfields and use much more fuel than a conventional take-off, leaving less fuel for the mission.