I can't speak directly for advanced lifters, as I don't have experience training people at that level, but tempo work can be helpful in certain circumstances (mostly technique/tightness). I don't personally see much use in a tempo concentric, despite some coaches I respect using them, but I suppose I could be convinced with a good enough argument.
This has nothing to do with Nautilus, MEH. Stop trying to shoe-horn stuff in.
Nor yet does it have anything specific to do with Superslowtm.
My point was about how some earlier strength gurus like Jones and later Hutchins espoused slow repetition movements, especially on the eccentric portion of a movement, was the shit hot ticket for being big and strong and cut and . . . Anyway, it'd cure what ailed ya.
It's really all about artificially imposing timing on the repetitions in the movements, 2/4 in Nautilus and 10/10 in Superslowtm. Most people found those protocols to be unproductive and dead ends. Although now, with all the nifty apps you can get for your phone, it'd be easier to wait for a beep tone as a cue rather to move concentrically or eccentrically than counting to one self. So I guess there's that.
My understanding of eccentric tempo and paused work is it provides some intensity without burning out the CNS or leaving the lifter too under-recovered for future training sessions. Lighter than normal weights are used because the tempo or the pause makes the movement more difficult. It is not used exclusively, but in conjunction with normal training. I.E. - If you squat 3x/week the middle session might use this technique. It is an advanced technique and not for beginners.
Guys, don't question Herbison. He has been a member of the Cool Kids Training Forum since Nov. 2017. Their training knowledge is superior to all others.
Couple reasons.
1) Technique. You get to directly practice the movement you're trying to improve, and you get more time to focus on doing it right.
1.a) The argument against that, of course, is that timing is also part of the technique, and you're screwing that up. I don't think that is really an issue with the eccentric, since it's not a substantial change. But I do think tempo-ing the concentric messes with the stretch reflex enough to have a negative impact.
1.a.1) That last part is why I'm not as concerned about tempo-ing the concentric on deadlifts, since you don't have a stretch reflex there to start with.
2) Lighter variation. Similar to what skid said, though I wouldn't use his phrasing. Most of the time CNS fatigue is discussed, the conversation turns (to borrow Hanley's favorite phrase) "hand-wavey".
3) Various others. 1 and 2 are the main, most common reasons, but there are a bunch of other situationally-dependent uses. For example, heavy, controlled eccentrics have some decent evidence behind them for tendon rehab purposes, though my own experience there is admittedly mixed.