Currently, the Baron and his ilk don't do anything that couldn't have been handled by your Mayor, and even then he's only useful two-three times per year. On a related note, Mandates are a vexing concept where the only motivation for doing them is that you don't want a random, potentially useful dwarf to get hammered or jailed or beaten.
Being such high nobility, the Baron should hold some pull, not only in his fortress but with the mountainhome, or even with nearby friendly towns. His opinion of the fortress he resides in should be tracked and shared with the mountainhome, in such a way that there's more to how many migrants you get than the merchants saying "Hey, guys, this place is RICH!"
What I'm suggesting is to have mandates (and possibly the Baron's living conditions) affect his overall 'opinion' of the fortress, and let him know what the fortress is or is not capable of producing competently. Many successfully completed mandates of the same type (say, silver items) would make him happy and tell him that the fortress can make plenty of these things, so when the caravan next arrives, he can tell the liason that this fortress is home to hard-working dwarves who could probably find work for some skilled artisans, especially metalcrafters. In following immigrant waves, you'll be more likely to get dwarves that can work silver, and perhaps some of your migrants will even have skills above novice/no-label.
Similarly, failing to fulfill mandates repeatedly (as in, glass items) will tell him, once he gets over his disappointment, that the fortress cannot make glass items. He will tell this to the liason, and so you are less likely to get glasscrafters.
It could also convince the baron to stop making Glass mandates and find something else to ask for. Naturally, his opinion of the fortress will fall, affecting your future migrant waves, until he begins asking for something you CAN fulfill, but the Unfortunate Accident ever remains an option if it gets too bad.
For this to work, the way mandates are chosen couldn't be limited to what the noble likes, instead either cycling through random object types ("this year, the fort shall produce leather goods!"), or based on what the trading liasons have requested for the year ("they want metal goblets and prepared meals, and so you should make some"). Granted, I haven't mentioned the Mayor or Tax Collector at all as far as mandates go, but... I'm sure we could think of something.
-Summary:
- Mandates no longer based on what the nobles like, instead being centered around periodically changing themes.
- Baron's opinion of the fort affected by his living conditions and the fulfillment of mandates; Higher opinion means more and/or more skilled migrants; merchant profit no longer the only deciding factor.
- Failed mandates means fewer mandates of that type being issued, and fewer migrants of that job profession arriving.
- Tax Collector, Mayor should probably also be affected somehow by the mandates issued, or alternatively will stop issuing mandates at all.