This may shock you, but Nasus isn't a late game champion.
Seriously.
Nasus has infinite scaling, and this is why people cite him as being a 'late game' champ. But, when you think about it, we have late game champions; adcs and several bruiser carries. They're champs who have insane steroids, powerful ratios, and who's kits mesh together to over-buff particular aspects of them, so that they scale heavily with items.
You don't give infinite scaling to a champion like Tristana, who becomes a literal god among men when she gets full build. You give it to a champion who has a strong early / mid game, but has absolutely nothing going for them late game... Like Nasus.
Nasus has always been strongest in the mid game, where he's tanky enough through base stats and his ulti to soak a hit, and has his Q farmed enough to also dish them out.
Late game, when the team fights roll around, Nasus has generally been easy to deal with. Wither is powerful but he's slow and shit and all of his tankiness comes items and lifesteal, both of which aren't terribly difficult to handle.
With that said, Nasus is absurd right now. The Q CDR on his ulti is insane, and once he hits six he's probably the strongest duelist in the game. He does need nerfs, but it's not because he's a late-game monster with a powerful early game (heyo, vayne).