Look all these things are fine - but think about their use, reason for use and effectiveness, and use of time… and IMO, in each case, there’s far better ways to use ones time to achieve better results.
What we must take into consideration is the following agility movement pattern split:
- Transitional movement (backward run, shuffles, slides)
- Initialization movement (drop step, cross step, cutstep, first step…)
- Actualization movement (skill/technique, sprint)
(Jeffreys, 2006)
This is higly dependent on a game/sport!
What I want to say with this? I want to say that lateral stuff are allmost allways submaximal in nature and represents a transitional movement during the athlete “waits” for a stimuli from environment/opponent. Thus, it seems that there is no need to do “LATERAL training” with high speed or with great load. This movements should be covered by quality sport practice. Practicing this under load may teach a player awkward movement patterns and screw his technique.
Thus, it seems that sled-loaded defence slides are poor choice of training, but…
if we try to train involved muscles with some more general means that not mimmic sport technique, then it may have a purpose. Couple of things come to my ming: single leg work, LATERAL sled pulls (walking, not mimmicking technique, and if mimmicked then with great quality done), band work(?) and general strenght training. Surelly, if athltes experience great specific stress with their sport practice, this kind of training must be reduced. Also, a lot of athletes have weak/inhibited glutes, and along with some corrective exercises slow lateral sled pulls may have some purpose…
Thus to conclude: transitional movements are mainly submaximal in nature and there is no need to specifically train them with great load/speed. Quality technique should be covered in sport practices, altought some general stimulation/strengt work may have some purpose.
When it comes to initialization movements, then plyos (single leg work, decceleration-eccentrics, lateral/linear/rotational) and single leg strength traing comes to my mind, along with normal strenght training and skill work (sport practice). I know a lot of you will not agree with me here, but that is ok and normal… 
I have my brain to think and I have my opinions, altough I am open to listen and learn. Please, when I said single leg plyos and NOT reffering o single leg depth jumps, but rather to zig-zag bounds etc
Actualization movements are sport techniques (dunk, throw…) and SPRINTS! Why should one backpedal for whole court when can turn and sprint? Thus sprint work is very important in “agility” as CF have pointed out numerous times.
When it comes to cone drills and agility ladder, and more leaned toward Charles Poliquin and Charlie Francis: avoid them (except in testing, warm-up etc). Thus mine philospphy of agility development is pretty simple:
Sport skills + game-like conditioning games + tag games
General strength (+single leg stuff)
Plyometrics (+single leg)
Short sprint (+hills, +sled)
When AST comes in? In general strength component as outlined… to streghten involved muscles in general way! Also, core stuff and ankle work can be done wiht AST along with some othe modalities…
- Jeffreys, I. Motor Learning – Applications for Agility, Part 1. Strength and conditioning journal. October, 2006.