"Can", yes. He "can" do a lot of those things but oftentimes he really just doesn't. I'm still baffled by him being strong these days, but that's partially because I continually underestimate the Kleptomancy keystone, it seems. And taking the Resolve tree as a secondary tree lets you start with a stupid amount of health.
Hit Klepto if anything, Nasus is pretty fine. Even after his 'OP' changes in 7.15, with Fury of the Sands (R), reducing his Siphoning Strike (Q) cooldown by half during it, and Spirit Fire (E) shredding a percentage of armour instead of flat, his win rate spiked from 45.8% to a huge 49.3% (according to op.gg). And he stayed around there, though lower, until patch 7.24, finally coming above 50% win rate. Which is also due in part to quite a good few folks who would have bullied him out of lane just not having a good rune setup anymore.
Any sort of concentrated crowd control just ruins his day (which, yes, is the same with any champion, but like most juggernauts he's particularly hurt with it). To damage something with everything, aside from his Spirit Fire, he has to be up close and personal with you.
His only reliable method of catching up to you is using Wither (W) (which is single-target, low cooldown, yes, but single target); and with MS-boosting items such as Talisman of Ascension (being removed), or Dead Man's Plate (which takes time and resets the boost on-hit). If you're fighting him 1v1 after a certain point unless he's behind or you're far ahead it's downright silly.
He excels at being able to duel individuals, which comes at the cost of having pretty much zero ways to spread damage across multiple people without killing one at a time.
And any stacks you gain on him past, like, 800 or so, really don't add too much comparatively (0.375% additional damage @ 800, 0.333% @ 900, 3% @ 1000 ... reducing the more he has). Since you're spending those on gathering more (likely on minions) instead of making proper use of them (on enemy champions and/or towers).
Nasus' stacking rate was increased from 2/4 per kill to 3/6 per kill ages back and he was still seen as trash back then. The reason Veigar gets stacks at the rate he does, is because of a few things:
- He gets a stack per champion hit by any ability he uses.
- He can hit two things with his Baleful Strike (Q), quite often getting two stacks per cast. (More if he kills a large monster or large minion.)
- He gets five stacks on champion takedowns. It used to be just kills.
- All of Veigar's abilities are ranged, he doesn't need to put himself in as much danger as others.
- Ability Power affects three abilities for Veigar. (Q), (W), (R)
Whereas Nasus:
- Only gets stacks on killing a unit with a Siphoning Strike autoattack. (Doubled against large monsters, large minions, and champions.)
- Only can hit one target per Siphoning Strike. (It only is applied to his primary target, not anyone hit by Iceborn Gauntlet or Tiamat AoEs.)
- Nasus has to be in melee range to make use of those stacks. (Amplified by Fury of the Sands' bonus range.)
- Siphoning Strike's stacks only amplify Siphoning Strike's damage, not affecting anything else in his kit. (Soul Eater (P) and Fury of the Sands affect Siphoning Strike, though. Not the other way around.)
I wish people would stop sensationalising a champion's possibility to oneshot someone because in many cases they just can't manage it. Sure, Nasus has a very, very scary spike of damage when he gets to you to use it, and to get to that point he has to spend the whole game hardly influencing anywhere else.
If a Nasus is getting out of control, cripple his team. If they die too quickly for him to take advantage of you fighting them then he can't do much without risking himself dying. Trying to stop him, but letting his team rebuild a lead, is one of the things that many intend to do. They know he draws incredible pressure just by being him, and they intend to make use of it.
If he's doing 1000 damage to you per autoattack, then you're a squishy. If you're a squishy and he's in your face, either you were alone, inattentive, or he got a good flank off and ambushed you. Or your team just didn't pay attention as he waded through them.
If you want to hit his Q stacking rate then you'd best prepare yourself for a bunch more E-max Nasus played, which was absolutely horrendous to go against if executed correctly. And I don't think anyone wants to see that being the popular thing again.
being strong and more about other bruisers that used to dumpster him having no keystone like 
for example, while 
vs ad or 
vs ap, he no longer is in any danger of dying 1 vs 1, and once he has 
, he will just take over the lane completely.