what prevents direct imaging of extrasolar planets, other than angular distance from the star?

It is simple.

Planets are not emitters of light. They only reflect light from their own sun.

When such a planet is on 'our' side of its sun, its illuminated face is facing away from us. It would be invisible.

When such a planet is on the far side of its sun its illuminated face would be facing toward bus so it would be visible to us, but it would be difficult to see because of the huge amount of light coming from the parent star.

The above situation refers to cases where the plane of the planet's orbit is seen edge on by us. In that case we observe the greatest angular separation possible between the star and planet.

The problem is that there is currently no telescope in service that is capable of resolving the planet's feeble light from the star light.

And just to put it in perspective. It is exceedingly difficult to observe dwarf planet Pluto from Earth. And that is against a black background. Planets orbiting other stars than our own are vastly further away. The next nearest star system is Alpha Centauri which is about 7000 times further away than Pluto.

The planets themselves are very small. We're talking about objects much smaller than 0.6 arcseconds, so it doesn't impress very much on a pixel -- the signal-to-background ratio is of the order of 1 (or worse). And this is admitting that you have a "perfect" atmosphere (or none at all, such as space-based telescopes) which doesn't distort the light path or absorb or disperse light...

Your best bet is to observe oscillations in the main star, and do some statistical analysis to determine the perturbation. The "correct" perturbation accumulates gradually when you increase the observation time, whereas the random background (which we affectionally call "noise") accumulates randomly and therefore doesn't contribute to the signal.