<p>What are the methods to auto eject parts (into a collection area/box/basket) in order for the 3D printer to continue printing?</p>

<p>For some reason this feature isn't common (yet?). Is there a hidden reason why?</p>

<p>Will using the print head to ram the part off the build plate into a basket nearby cause the print head to misalign (if using belts).</p>

<p>I am planning to use a Cartesian XY-Head type (like CoreXY) printer, where the build plate moves along the Z axis and XY axes are on the ceiling of the printer using belts to move the print head.</p>

From the standpoint of a hobbyist user with a mid-range machine, my answer is based on the model release from the build plate. With a heated clean glass plate, my model will
almost
always release once the plate has cooled. The "almost" aspect means that if you want to use the print head to push the model clear, you will be confronted with a stuck model occasionally.
The amount of force applied by the head may be enough to release a stuck model, but "may be" is not going to be sufficient. Especially with a core-xy system (used by my Emblaser laser engraver), you can either toss a belt or cause a stepper motor skipping. More powerful motors will reduce the skipping possibility, but not the belt jump problem.
You could consider to add one additional motor with a sweep arm, geared in such a manner as to provide the necessary torque, along with a force sensor to register a model stuck so badly as to be impossible to dislodge.
Your g-code would be written to lower the bed to the appropriate location to allow the sweep arm to operate, while the force sensor would be tied into the pause/stop circuit of your controller.
Some controllers already have the ability to manage an additional motor, as some are manufactured to provide for dual extrusion.
If such unattended operation is going to be a requirement, you'd also want some form of aborting a failing or failed print.