Super Saiyan said:
It was Shanks that pointed out that he never slept in Oden's flashback. That was well before he had a fruit.
Then maybe he doesn't sleep not BECAUSE of the 2 Akuma no Mi, but he has 2 Akuma no Mi BECAUSE he CAN'T sleep. This allows him to have these two Devil Fruit.
Crazy theory now, but when Black Beard was shown as a kid, he was shown crying and thinking about the night. So he was likely sad that he couldn't sleep:
https://www.google.com/search?q=black+beard+kid&client=tablet-android-samsung-rev2&prmd=isvn&sxsrf=ALeKk02xB9gBFdOuIy4CXmbmTi1XYbfe0Q:1616533974865&source=lnms&tbm=isch&sa=X&ved=2ahUKEwjN8NqqqsfvAhX3IrkGHd8VAdwQ_AUoAXoECAcQAQ&biw=1280&bih=800&dpr=1.5#imgrc=2bHdjxP62BPO1M
When in Drum island, Luffy told Sanji that people from snowy countries don't sleep, since if they sleep they die. And that's precisely the island BB attacked. So maybe Drum is the native island of BB.
There's a certain disease known as Ondine's CURSE in which the bearer of the disease can't sleep or will find problems sleeping otherwise he may die.
https://en.m.wikipedia.org/wiki/Central_hypoventilation_syndrome
Maybe BB was a bearer of such disease and tried to find apt doctors in Drum island to cure him? Drum island is known as an advanced medicine country. He didn't find doctors (since Wapol took them) and destroyed it. So because he can't sleep, he can allow himself to have 2 Akuma no Mi, since the powers of them won't clash, won't diverge.