To me slugs and buckshot serve very different purposes, so combining them in one shot doesn't help me any.
I keep buckshot loaded for in my house (up to 10 yards) without too much over-penetration. It would likely stop at my siding, if not at the siding of another house (and that's if I miss my target).
Slugs are around for longer range shots and will defiantely overpenetrate a two-legged predator, and probably other houses in my area. I would keep slugs loaded if there were no other houses around or I was defending against large four-legged predators (in which case I wouldn't want to waste space with buckshot, I would want the biggest hunk of lead I could fit).
Birdshot seems ideal for houses with people in other rooms on the same level as you (an apartment complex, or adjacent rooms with kids in them).
Keep it simple. Personally it frustrates me when ammunition companies (and certain gun companies) take something like self-defense with deadly force and try and market "gimmicks" based on no ballistic or factual data. It is irresponsible and misleading.