Is it possible that the reason why regigigas has this ability is because it's has been sleeping for so long? Sorta like the "I hate getting up in the morning" kind of thing?
Slow Start is given to Regigigas for the same reason Slaking has Truant and Shedinja has 1HP. It is there to intentionally, although temporarily, cripple a Pokémon that would otherwise be extremely dangerous. You'll see this guy in doubles a lot, paired with someone who can change its ability. The game makes it hard for Regigigas to stall its opening turns - it's one of very few Pokémon that can't learn Rest for this reason.