Unbound Corsair Army question

Do the Prince's path options which refer to detachments still confer their bonuses in unbound lists? This isn't a command benefit so it shouldn't be negated by the unbound rule wording, but I'm unsure if other units can even purchase the obsessions benefits RAI.

BRB(p117) "If you used the Unbound method, then once you choose your Warlord, every model in your army that has the same faction as your Warlord is considered to be part of the Primary Detachment for all rules purposes. ...these models are not bound by any Detachment restrictions and do not receive Command Benefits."

I read this RAW as not only permitting multiple Princes per unbound army, but multiple Princes who treat each other as being part of the same detachment for obsession purposes. When an obsession purchase checks for the detachment question in unbound it's answered by a faction check, which is all Corsair.

Thoughts? Correct me if I'm wrong.

This should be in the rules subforum not here.

That said after re-reading your argument 3 times I have concluded that I believe you are absolutely correct, I even think the do not receive command benefits bit is relevant. Your argument stands on it's own from the first clause.

I'm not sure if it would be worth it, but definitely totally legal in a non-battleforged only environment.

Thanks for the support! Yeah I wasn't sure where to put it since the rules forum seemed more geared to DE alone.

As for utility, I'm not sure yet how best to use it either. It would be for a 750 pt unbound fight club tournament at my FLGS.
But 6 Princes each with
Jetpacks,
Combat Drugs,
Mastercrafted Void Sabers,
Multiphase Key Generators,
Shadowfields,
5+ Feel No Pain,
Rage and RotOD shenanigans,

and with an IWND, a Rampage, a Cegorach's Rose, and a Mastery 2 Malefic Wild Psyker thrown in... I'm sure I could think of something.  I want to say you could fully kit 6 of them out for under 1200 but I have to check the math on that one.