High-edge characters tend to throw it around a bit more, while the low-edge characters are a bit stingy with it. The real knocker is that, no matter what, most PCs should have that last point of edge saved to burn "just in case".
A character can choose to burn a point of Edge - permanently reducing his Edge attribute by 1 - for one of the following effects. . .
It's arguably an interpretation preference, but the way I read the above, they don't need a point of Current Edge to Burn a point of their Edge attribute. Just my 2¥.
I've thought of doing it this way as well, but since it's never come up in a game, I haven't needed to worry about how to interpret that rule yet.
I'm not sure on the Wild Dice idea. If you spend a point of Edge, all your dice explode. Ergo, if you put the wild dice in there, chances are players won't be spending any Edge at all because they probably won't need it.
Well, when you spend the Edge, if you spend it before you roll, you add the extra dice (in voyd's example, 4, for a total of 16) and ALL 16 dice can explode. Whereas, what voyd is suggesting is that even without spending Edge, a specific sub-set of your normal dice pool would always have a chance to explode, making your Edge stat (aka, Luck) more relevant roll to roll. So there's still an advantage (+4 dice, all 16 explodable) to spending the Edge. Even after the fact, you could add 4 more explodable dice to the roll if you don't like your luck.
While I don't think it's necessarily as big an impact as you might think and it does sound like a neat idea, I still probably wouldn't use it myself as I like the limited nature of the current Edge system. Also, I encourage my players to use multiple colors of dice to be able to efficiently roll several dice pools at once, so it'd make that aspect harder at my table. 
My main thought in this hypothetical house rule is that it would make people want to bother to buy more edge even if they were of the "stingy with character resources" type that has been mentioned, which I feel is a trend amongst most of the players I know. I don't feel it would weaken Edge point expenditures although I can see where this is a concern to be watched for. I think the idea for this house rule came to me when I was contemplating the optional rule for making the game more cinematic via making hits occur on 4s, 5s and 6s - which to me is way over the top. IMO, if that rule were used there would be almost no call for edge at all except for canceling glitches and hand of god stuff; all of its neat stuff would be ignored because of how easy tests would be. So I thought, "what if you could give the players an edge (no pun intended) without making the game ridiculously easy-sauce?" And that's when it popped in there that you could simultaneously make the game more cinematic via the "wild die" effect similar to SWd6, and make edge
more important in the process, rather than making it more or less obsolete.

Maybe I'll do a quickie game (like only 3 or 4 sessions) just to test this out. For Science!
