What you described there has actually a name
It's Continuous Collision Detection (see here for example: https://en.wikipedia.org/wiki/Collision_detection#A_posteriori_.28discrete.29_versus_a_priori_.28continuous.29 )
Most Physics engines have switches to enable CCD for certain bodies (e.g. bullets, rockets, stuff like that) but often have it disabled by default since it is more costly than the standard simulation.
Edit: This page has some nice graphics explaining the stuff as well: http://www.stencyl.com/help/view/continuous-collision-detection/