The real reason Edge has been getting so many title reigns lately is that he is all Smackdown's got. He got, 4?, title reigns in just over a year. He is a good wrestler who plays his part well, but I can't see him passing Triple H. Eventually Edge will start having long, more meaningful reigns and then the number will stop rising so fast.
I tend to agree with this part of your post. Edge has truly helped carry the Smackdown brand since he moved over there. The Undertaker is on a very limited basis, and while just mention of an Undertaker appearance still gets several hundreds, if not thousands to attend.. it's normally Edge and the performance he, along with several others, put on.. that keeps the fans coming back when Taker comes up missing.
As result, I do believe Edge will begin having longer reigns. And my theory on why he hasn't had any (outside of injury from two year's ago) is because it works better in his favor, to put over other individuals.. then capitalize by 'stealing' the title back at a short, later time.
On the other hand, he has alot longer in the business then Triple H, and if he can go until he's Ric Flairs age then it's a possibility he will get up to around 10-11 reigns.
Unfortunately, I don't think Edge will be in the business this long. He's been injury prone and as result, I don't seriously believe his body, namely his neck, will withstand another 10-15 years.
Of course, by then Triple H will be on reign 32(overexaggerating..maybe) or something, so I don't think Edge will pass Triple H, but he will get up there into the high numbers.
Triple H. is bound to break the record, if for no other mixed reason than..
A.) He's the W.W.E.'s standard Championship poster child.
B.) Ric Flair mentored him and likely would not mind at all that it were him, to replace Flair's historical performance.
That said.. it's not shocking, or too hard to think Edge might not at least come within 1 title reign short, of Ric Flair's. Just because of who Edge is in this business, and what he's come to mean to this industry.
He's (Edge) definately earning a Hall of Fame spot, regardless of anything else he'll accomplish.