With regards to competitive formats, a move that only lowers the opponents stats is much less valuable than a move that boosts your own. All your opponent has to do is switch out (which they're probably going to do anyway if they can't hit you Super Effective) to nullify the changes to their stats. Where as if you had raised your own stats, there's precious little they could do about it. Only making your Pokemon faint, or using a force-switch move (all of which have reduced priority) or a stat clearing move (Defog, Mist, etc) can negate that.
And honestly, comparing +2 to your stats against -2 to an opponents stats is going to be a loss most of the time. When you are raising your own stats, in most cases you're also putting investment into those stats (ex Attack with Dragon Dance or Swords Dance, Sp Attack with Calm Mind or Nasty Plot, Defense and Sp Defense with Cosmic Power), which amplifies their effect. Moves that lower your opponents stats, however, are much more hit-or-miss. If the target is a Sweeper, you'd get more mileage out of just attacking them and making them faint -- it's rare that they have put any serious investment into their defenses, so lowering them just wastes your time, which might hand them the victory. If the target is a Wall, you'd be more effective to switch to a Pokemon that targets the other defense, since it's rare for a Wall to be strong on both defense stats. Anything else is going to be dealt with more effectively by either switching to a defensive Pokemon that resists, or an offensive Pokemon that hits Super Effective.
And regarding Throat Spray, it is triggered off of vocal/sound moves. Acid Spray is more like Water Gun, rather than Boomburst. It's a liquid, not a sound. Screech, on the other hand, should trigger Throat Spray.