Why on Earth would you disallow a player to use Edge on his Addiction test? Unless you're using Missions rules, which require you to buy hits on "permanent" effects and anything that occurs in downtime, I see absolutely no reason not to allow one of my players to use the resources at his disposal for the benefit of his character...
I see 2 possible reasons: because addiction tests are too easily cheesed otherwise (if you allow Edge, you're already 80%-90% down the slope towards "allow them to them buy hits"), and because there is already a precedent for not allowing Edge on some tests:
This counts as the culmination of all your work over the days, so you can’t use Edge for this test.
Besides, the only instances where a player cannot avoid an Addiction Test are Jazz (TH 1, both), Kamikaze (TH 2, mental), Nitro (TH 2, both) and Tripchip BTLs (TH 1). Meanwhile, Cram still gives +1D6 Initiative Dice, lasts longer, is cheaper, and can be used 4 weeks in a row followed by a 3-week cooldown without ever having to do an Addiction Test.
Let's use Nitro, the most dangerous drug when it comes to addiction tests, as an example:
- Without Edge, someone with 8 dice on one and 11 on the other will have a ~74.45% chance of passing both tests, and that's without asking a Magician to buff you.
- With Edge, someone with a measly 5 dice on both tests and 2 Edge will have a ~76.44% chance of passing both tests. Turn that into 8 dice on both tests, and suddenly you're dealing with ~96.69% - and having 2 buff spells for 11 dice each turns that into ~99.6% - and that's for the most dangerous drug.
And keep in mind this is with Second Chance, which beats Push the Limit for minimizing the chance at few hits unless you've got like 5+ Edge and only 5 base dice (second example: with 8 base dice, 7 Edge gives you a 98.34% with PtL versus 98.33% with SC at beating TH 2 tests), so all you need is 2 Edge for drugs that require both physical and mental tests.
TLDR: there's precedent in the rulebook for not allowing Edge usage on things that take multiple days, and Edge turns Addiction Tests from something to actually worry about a bit into almost 0 risk, without requiring you to actually have more than 2 Edge. Plus you could always use Magic to boost your odds, or use Cram.