Could we dispense the near clipping plane? Would it be, at least theoretically, possible to render without a near clipping plane? Could raytracing ignore this perchance? 

Quite many budding 3d artists have a WTF moment the first time they encounter the clipping plane. If this could be avoided then it would be a big win for usability of 3D authoring apps. Its not one of those things a normal artist would think about until explained.
The near clipping plane in rasterizing setups with perspective projection is there to avoid a divide by 0 and bound the possible depths for orthogonal projection.

With a bit of extra math you can make the depth stored in the depth buffer linear again. However you still need the guard against the divide by 0.

In raytracing the near plane can be at 0 no problem. There is nothing technical stopping you from putting it at -10 however (besides that it would be very odd).