Or, "Why doesn't the duke just send his own henchmen, who are higher level than us?"
* Plausible deniability - dirty deeds are best done by assets you're not too fond of. Adventurers are not known for their discretion, as a rule, but sometimes you're working with what you've got.
* Praetorian Threat - if his domain-tier henchmen are Grudging, maybe he wants to make sure they don't level, and would prefer to keep them where he can see them.
* High risk - if his domain-tier henchmen are loyal and awesome, maybe he's unwilling to risk them dying to a lousy poison save or other bad luck.
* Duke Ackbar - it's a trap to get those damn troublesome adventurers out of the picture once and for all before they become any more of a threat.
* The Test - an experiment to figure out if he wants to keep these adventurers on permanent retainer and start integrating them into his domains.
* Opportunity Cost - the duke thinks that a political rival might hire the adventurers for some useful purpose, so he concocts a mission of marginal utility to him but which keeps them busy and out of the rival's employ for a while.
* The Long Haul - the mission is expected to be long enough that sending his own henchmen would reduce the stability of the realm (or the loyalty of those henchmen).
* "Unique capabilities" - this is the typical, beaten-to-death explanation; adventurers are Special and the only ones who can do the job. Mostly falls apart in ACKS, but there might be circumstances where it applies (ie, party with perma-flying wizard and a horn of blasting can get up to some unusual mischief).