Li Shenron
Legend
Advantage/Disadvantage is not the same as a +4/-4. Advantage and Disadvantage doesn't change the DC the person can hit, only the chance of actually hitting it.
This is the key point of the matter.
Adv/Disadv really serves a different purpose than circumstance bonuses/penalties of 3e. Both generically increase/decrease the chance of success, but also the latter enable/disable the highest DC.
I am not sure we really "need" circumstance bonuses in 5e. But circumstance (or whatever) bonuses could be used by the DM for implementing a (sort of) gamestyle where there are things you can do only if you get the right idea that gives you an edge, and turns an unreachable DC into a hard but reachable DC. Don't think about using this for stuff you need to do in order to progress in the adventure (the proverbial closed door that if you don't get past, you just can't continue the adventure) which obviously is a problem, but rather think of "unlocking" shortcuts, getting extra bits of information, additional magic treasures etc. You can still just roll for these, but at least I have used in the past the idea that e.g. that special magic sword can be found not simply with a high roll on Search, but the players needed a key idea to get that circumstance bonus. Overall this is still possible of course, by e.g. lowering the DC instead.