I don't know "the" explanation, but I can certainly speculate.
Relatives of the maleo bury their eggs in compost, so burying quite likely evolved before the maleo split from them. They bury the eggs in warm material, which has the advantage that the parent bird need not sit on the nest - which can be very dangerous for ground nesting birds.
So I'd suggest: Burial in warm material allows the parents to spend more time away from the nest. At this point the parent still looks after the nest and helps the young birds out. Some young birds are lost because they can't dig themselves out, even with help, but overall it's a plus.
This situation becomes more extreme. As the young birds get better at digging themselves out, they can be buried deeper and/or the parents need to spend less time at the nest. (This sort of balancing is expected in evolution) so the need to be able to dig ratchets up and evolves.
So:
Originally the young birds would have been helped by their mother. They didn't need to dig themselves out on their own.
As they got better at doing without their mother, so the mother's involvement declined (because the life of the mother is more important than the life of one chick). The mother would often be away when a chick hatched, and so the chick needs to dig itself out at least enough to breathe. I'd guess that this also produced a pressure for the chicks to be more fully developed when they hatched, needing less parental support after hatching - largely because the more developed chicks would be better at digging.
The process continued, getting more extreme. It was always an advantage for the chicks to be better at digging - but any improvement in digging can be exploited by the parent spending less time at the nest, for a greater overall advantage.
Now maybe I'm overlooking something but - on the little information I have - that account looks basically plausible.
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