This is an important point, so let's be precise here.
The fact that a reactor is fueled by waste doesn't mean it doesn't create waste or have a waste-disposal aspect.
There is nothing in the physics of building nuclear reactors that prevents us from building a reactor that does not leave behind any waste that is either chemically reactive, or even modestly radioactive. No currently implemented reactor designs do that, but it is possible to create one that is both fueled by current reactor waste, and has no waste disposal aspect.
It is unclear if we could ever license such a reactor given the current climate.
There is nothing in the physics of building nuclear reactors that prevents us from building a reactor that does not leave behind any waste
First I've every heard of any such proposal. How exactly would you go about stabilizing every last decay product to the level of background radiation?
Your statement is equivalent to noting that there's nothing in chemistry which prevents us from building coal-fired power plants which capture all CO2 and toxic pollutants (mercury, sulfur, particulates, NOX,, radioactives, etc.) as well. However it's economically and thermodynamically infeasible. Not that emissions haven't been drastically reduced from early designs, but it turns out that that's still not good enough.
Proposed designs go under the heading of 'closed fuel cycle reactors' generally a "fast" reactor (which is using its gamma flux to create new fuel) a reprocessing plant, and the power reactor(s). Such a facility runs "forever" with no radioactive or chemically active byproducts leaving the facility.
Even closed cycle systems generate low level radioactive 'waste' in the sense that things get activated by exposure to radiation. Traditional incineration, like these guys (http://www.nukemgroup.com/fileadmin/pdf/Brochure_Incineratio...) propose, reduces bulk and chemical reactivity, using ionizing radiation from a gamma source (another small reactor like the TRIGA) can move the radioactive byproducts along their decay cycle into short lived isotopes and then inertness.
The fact that a reactor is fueled by waste doesn't mean it doesn't create waste or have a waste-disposal aspect.
There is nothing in the physics of building nuclear reactors that prevents us from building a reactor that does not leave behind any waste that is either chemically reactive, or even modestly radioactive. No currently implemented reactor designs do that, but it is possible to create one that is both fueled by current reactor waste, and has no waste disposal aspect.
It is unclear if we could ever license such a reactor given the current climate.