He isn't one of the greatest of all time, objectively speaking. If we're talking tag team wrestling, then sure, he and Christian are definitely in the GOAT discussion there, but as a singles star, no.
The reason why is basically because while he was good in every category that you can use to measure and quantify a wrestler's worth or success - drawing power, in-ring skill, promos, etc. - he wasn't the greatest or near the top of the list in any of them. He didn't draw industry changing money the way Hogan, Austin and Rock did. He's also not been the top face or name that has lead an era the way Cena has. He isn't a Kurt Angle/Ric Flair/Shawn Michaels/Bret Hart/Chris Benoit caliber performer, so whenever the true greats as far as ring work come into the discussion, Edge's name won't really be brought up. He is very good on the mic, but whenever you start to have a debate about the true greats of working the mic, then Edge will certainly be below Hogan, Austin, Rock, Foley, Dibiase, Piper, Cena, etc.
Realistically, since GOAT = Greatest Of All Time, there should really only be maybe a handful of people at the most to debate over in each category. There can only be one greatest, after all. Does Edge crack the top five or ten when it comes to the biggest stars in wrestling? Does he crack the top five or ten when it comes to being a great in-ring technician? Does he crack the top five or ten when it comes to being a great talker? I would argue No.
He was a very solid performer and talker. He had a natural rise to the main event - he was a great tag team wrestler, then great in the mid card, then a competent main eventer, and he retired as one. He won several championships and has quite a few noteworthy accolades to his name. But all of that doesn't really make you one of the absolute greatest. Sheamus and Del Rio are the two biggest flops of the past several years, are they 'great' just because they have several kayfabe victories and accolades to their name as well?
IMO, to be considered "one of the greatest", you should at least be in the top ten or fifteen when it comes to being the biggest star or having the complete package, and I don't see Edge as being in that category.