So the usual problem with Infestation and friends is that your opponent gets the opportunity to switch in a counter, right? This can actually be used to your advantage by running a trapping set on a pokemon that doesn't usually use one in order to lure specific targets. A moveset of Trap/Protect/Substitute/Attacking move with a Binding Band can handily take down some opponents without even giving them a chance to respond: Four turns of Binding Band trap move will remove 66.66% of the opponent's health, and can be stalled out with Protect, Substitute, Protect. On something like Accelgor that can Substitute before the opponent attacks, the only real problems are outspeeders (scarf, STRONG priority), phazers, and opponents packing a recovery move (although if you can predict the recovery it'll net you a free switch-in!). Gengar is another amusing option, although opponents will be expecting to be Shadow Tagged which means it's a lot harder to catch something that wasn't expecting to be caught.
The other option is to grab something bulky enough to cop a single hit from common counters and simply accept the damage on the second turn (this has the advantage that your fourth move can smack them for additional damage). Or you could just do both and use Tentacruel, which will conveniently lure in and promptly murder spinblockers that it would otherwise lose to. Zygarde is another solid choice, boasting solid bulk and reasonable speed (although Bind is not completely accurate). Dragonite gets access to Bind from a Move Tutor and is extremely difficult to OHKO thanks to multiscale, too. Scolipede has poor defenses, but will have +2 from Speed Boost if you successfully threaten an opponent out and Protect, allowing it to outspeed nearly everything (and it's not weak to any priority attacks either!). Spiritomb is, as always, a royal pain in the behind to actually kill. Dusknoir is an excellent candidate, boasting a solid Attack stat, STAB that isn't resisted by much since Steel lost the Ghost resistance, and the ability to force quite a few things out. And finally, Quagsire has a unique niche amongst defensive users in that the opponent can't simply boost on your Protect turn and then beat you down turn 2, thanks to Unaware. However, it does tend to lure in things capable of OHKOing it.
In summary, binding moves allow many pokemon to handle opponents that commonly switch into them by essentially frustrating them to death. This lets them act as good lures for specific opponents or even broad classes of enemies, sniping or at worst severely weakening key opposition members to set up for an ally.