I have no idea if SlingBox is compatible with all the DVD juke-box style DVD players. One could probably ask them what is known to work.
[1] - https://www.slingbox.com/
[2] - https://www.amazon.com/Sony-DVP-DVPCX777ES-Disc-SACD-Changer... [example, not tested]
Consider for a moment that Netflix offered that service, how would you choose the menu options on that DVD? You'd have to wade through all those copyright warnings and adverts you can't skip. You'd have to pay more for the power consumption of the DVD player. Consider if every consumer had this service, how big would their warehouse have to be to store all the DVD players along with their collection of DVDs to play?
It would be a logistical nightmare for Netflix.
Edit, See: https://en.m.wikipedia.org/wiki/Aereo
Probably no beueno