The BAB isn't just good for getting that fourth attack by level 20. A binder's role in combat is mainly that of a secondary beater, and they can be pretty good at it too. (I've tried playing it as an arcane caster sort of role, and even with an obscure feat to get UMD as a class skill it was still pretty rough in combat.) Since pact augs are fairly spaced out, going into KotSS gives you an immediate boost in offense that can pay off even in the middle of a campaign.
The outsider type change is good, but generally not that important unless your DM doesn't allow Zceryll. If you are allowed to use Zceryll, odds are you're going to be binding her more often than not, because holy BALLS is she fantastic, and among the fantastic things she gives you is the pseudonatural template. Which makes you an outsider. Along with DR, SR, elemental resistances, 1/day True Strike, and an alternate form. And then on top of that you also get telepathy, mindsight, dazing rays, bonuses to saves against mind-affecting stuff, and, oh yeah, summons. All of the summons.
Zceryll is a little OP. But I digress.
Becoming an outsider, kind of nifty. But the main thing you want to get level 5 of KotSS for is the vestige's surge. Once per day, ignore the cooldown for one of your patron's once-per-5-rounds abilities.
This is HUGE. Seriously, I don't get how you can have played binders before and not realize how great that is. Even though it is just 1/day, that means in those crisis situations where you really, really, REALLY need to use that ability again RIGHT THE HELL NOW...you actually can.
That said, it's probably not quite such a no-brainer as the charop folks say. Losing out on mind blank is kind of meh (few campaigns run that long in the first place, and you can get continuous mind blank much, much earlier by binding Haures, whose other granted powers are pretty nifty as well), but delaying your access to the immunity to energy drain and negative levels (or losing it entirely, depending on when the campaign ends) can really hurt. As can, believe it or not, delaying or losing a bonus feat. Binders are a little feat starved, and sometimes a bonus feat, even from that very limited list binders get, can be rather nice. And if you're not too big on the attacking stuff, delaying/losing a pact augmentation can be bad too, given that augmentations can be used for more than just attack.
All in all, I'd say the charop folks put a little too much weight on the full BAB and cooldown ignoring. It's a very solid PrC, but not exactly the no-brainer it's touted to be. Really depends on your campaign and playstyle.