NIN shouldn't need to throw up DE with a WAR present, MT or OT. Sometimes there's situations where getting aggro on something that's freshly spawned takes priority over applying SE (in which case the NIN will want to start with DE and then the WAR applies SE from then on), but otherwise SE should be up 100% of the time.

Let's take a quick look at each combo and what it does:

HS -> SS -> BB: Aggro combo. Has extra enmity modifiers on the last two abilities used and will give you a massive amount of aggro, especially with buffs up.
HS -> Maim -> SE: Damage buff combo. Applies your 2 most important damaging buffs, Maim and SE. This allows for higher DPS, and therefore higher aggro generation.
HS -> Maim -> SP: Enemy damage debuff combo. Reduces damage output by the boss, very useful in progression content and before tank busters as a CD.

So, now that we know what each combo does let's work them into rotations.

SE -> BB: Highest damage/aggro generation possible. This is specifically used when SP isn't needed (aka farm content).
SE -> SP: Highest damage possible while keeping up SP. This is fantastic in progression content as it allows you to output high DPS and still maintain SP.
SP -> BB: Lower enmity generation than SE -> BB, lower damage than SE -> SP, but highest aggro generation while keeping up SP. Only useful in progression content where aggro is an issue.

I personally never use SP -> BB. It isn't horrible, it works as it's intended to work (aggro generation + SP), I just have never had a reason to use it. After a fully buffed SE -> BB -> SE opener I will either rotate SE -> BB or SE -> SP. If I'm ever losing aggro with the latter, I'll prioritize BB over SP for 1 rotation and then continue as normal. SP -> BB also forces the NIN to apply DE, which will lower their DPS.