I was thinking that if you made the engines generate lift it might help a tiny bit with the amount of time to takeoff, and thus lowering runway lengths.
Good thought, and it does happen. Tilt the jet exhaust or propeller downwards at a shallow angle $\phi$, and there is lift created at sin $\phi$ while thrust is reduced by cos $\phi$. If we take small angles, let's say 3 degrees:
- $\Delta L$ = T $\cdot$ sin(3°) = 0.052 T
- $\Delta T$ = T $\cdot$ cos(3°) = 0.9986 T
So 5.2% of engine thrust is converted into lift, for a loss of 0.14% of horizontal thrust. Free lift! Slight angles like this are found in aircraft installations, for instance in tail mounted jet engines which are angled horizontally to reduce yawing angle with a failed engine.
With engines mounted underneath the wing,the downwards pointed thrust would help a tiny bit in lift and reduce the take-off length. As @mins points out, with tail mounted engines the nose down pitching moment may counteract the lift benefits.