"I thought that BA's are really more concerned with communicating the business requirements (either in BRD's if waterfall or as user stories if Agile) and then it would be up to the developers to break down the business requirements into the tasks/steps they need to achieve those requirements."

Not always that simple ...

The work package represents the list of tasks or "to-dos" to produce a deliverable within a project.

Sometimes the developers are contractors and don't know the what the system is or what it does or how it works ... they are the coders to get your system changed. They are hired to come in and do the needed work and go home.

Detailed documentation will be waiting for them, telling them their log-ins, where the programs, tables, etc. are located. There will also be company coding standards to follow (so somebody won't go off the deep-end with erratic coding), testing environments, change-management procedures, etc.

There is usually an intro meeting with the contractors giving them the Big-Picture of the system, what they will be doing and who to contact ... kind of a Kick-Off meeting for the contractors. If off-shoring, their company contact needs to be there and do any translation needed. Rules, Regulations and if a Health-Care system ... information on HIPAA / HITECH - Privacy, Confidentiality, Security.

A Business Analyst can be a Busy Person ... Not just writing stuff and handing it off.

No.  Unfortunately the term 'BA' is incomplete.  The discipline of a 'BA'  is that of business-systems analysis and design.    A BA is not a scribe.  You look at a system, understand it, understand what function is meant to perform, understand why it isn't right, break it down completely and re-design it.... better.   A BA is much more a detective, architect and solution finder than a recorder.  A BA's main task is to improve or re-invent the design of the system, irrespective of the physical implementation; then proposes options for implementation.  The programmer works out the best code to use to achieve that.  
In the building industry we have architects who speak with the client wanting the building and finds out what they want  --  3 bedrooms, 2 bathrooms, kitchen, basement, etc. But the client doesn't know how to make it happen, how to lay it out so it works smoothly as a space for people, doesn't know the ceiling heights for the basement level pool and wine cellar, doesn't know that tall ceilings in the basement make it look like it isn't a basement.  That is for the architect; and it is not for the builders, electricians, plumbers to decide. They might know it too, having worked on other projects like that, but they should not be expected to decide that the basement will have double-high ceilings. They build according the the architectural specifications. Otherwise the whole thing is less likely to have any specific architecture at all; or it will but who know what builder will decide it, if any.  Of course, it happens often the builders may have a ideas for how to do things in an easier way, or that the design is just crazy.  In which case the architect and builder have a conversation.