Playing the lottery and winning every day can make you a billionare in a couple of weeks. If you're lucky.
The odds of finding a BoE epic actually aren't too bad. If you have a 0.09% chance to get one with each kill, it would take about 2,500 kills for a 90% chance at at least one BoE ilvl 665. Plus you get a few bags full of greens and a couple blues, along with ~0.5g per kill.
If you assume 250 kills per hour (about what my grind bot gets, IIRC), then you have a statistically probable chance at getting one after 10 hours. If odds are in your favor, expect to get them a little sooner than that. You will also get ~1000-1250 raw gold and ~800-3000g in other items. Also if you assume you run a bot 24 hours a day, it works out a little more favorably:
24 hours BoE farming:
3000 gold
1900-7200g in blues/greens
60,000-120,000 in epics (depending on realm--mine go for 30-60k each depending on which one).
This works out to 65k - 130k per day, or 2.7-5.4k/hr in the long term. Given that the low end is still twice as profitable as instance farms, I think it makes a lot of sense to farm BoEs right now. Even if you're doing it by hand, it's probably better than farming mats.
Significantly better odds than a lottery, but then again so is being killed a vending machine. Although I do agree with you that this might not be the best method for someone wanting to "safely bot" on their main (ignoring that this is a logical fallacy in itself).