It's a manager's job to make sure the team is able to get work done efficiently and in coordination with the rest of the organization. At the highest levels of the organization, it may be the manager's job to represent and speak for the team, but only when this makes the team more efficient. It may not appear so, but cross-department communication may very well be frequent enough and detailed enough that your manager is doing a disservice to the team by not delegating it. It could very well be just as dangerous as your manager trying to do detailed technical work, like taking hands on responsibility for major feature development.
A way to judge this is - when you do the work, figure out what percentage of your time this took. For example, if the various emails, meetings, phone calls etc takes 4 hours a week, then it's 10% of your time. Then multiply by the number of people on your team - if you have people then if 1 person (your manager) does this stuff, it will take 50% of his time. Is your manager doing this work the best use of your team's efficiency? What else should he/she be doing? Hopefully the manager's work also includes - helping people get better at their jobs, planning the next pieces of work, keeping annoying external people away from the team, developing ideas (hopefully with the team) of better ways to do work, being part of the biggest crises, watching the financial impact of how the team is working and what value is being delivered. If 50% is spent on external communication with other departments, is there enough time for the rest of this work?
Based on my experience 50% of manager time allocation is unacceptably high and a good sign that work like this should be delegated. 10% or less means that it is odd enough and happens rarely enough that the manager can afford to keep it as his responsibility. It's easy to see only one frame of reference - if you are only just starting to do it, it will seem rare, but it can be the case that:
- some teams do this all the time - I had a team where 90% of my individual contributor's day was spent on the phone with other corporate entities or people in other major divisions of our organization around the country.
- individual contributors growing in their careers must do more of this to succeed. Often the distinction is becoming senior level - the new folks aren't trusted yet to talk to bigger parts of the organization, so seniors take the responsibility.
- the work is truly rare and really can be done by the manager, because it happens once per quarter across the entire team.
Times when it should not be delegated
I think of this as a litmus test for when NOT to delegate.... don't delegate, or support delegation very cautiously if:
There's a high risk of damage from poor technical decisions
There's a high risk of damage from poor communication resulting in damage to trust in relationships.
The person being assigned the work is seriously at risk of not being able to complete it successfully.
This is true in almost all kinds of delegation, but organizational collaboration assignments have the middle bullet more strongly - a team will remember the personality of another team, and it's particularly risky when it's first-contact situation, or when there are reasons for the organizations to be poorly aligned (for example, if both are competing for work in this area, or if they want opposite things).
Delegate but support
Managers should always support their people, but sometimes that support is not overly visible. A manager may do some or all of the following in a situation like this:
(visible) - Kick off Mail - an email to the assignee and the other parts of the collaboration introducing the assignee, the scope of the work, and the other parties, and then clearly handing off the work.
(not visible) - a sync up with counterparts in other organizations - a periodic meetup with peers in other parts of the company, usually with an agenda of incoming work and who will be doing it.
(visible) - Personal intros without specific tasks - taking the potential future assignee long before the work comes along and introducing them to counterparts. Ideally this should include some inkling that there will be future collaboration
(visible) - coaching on style - giving some specifics on exactly what communication format/key elements are in the work.
(invisible) - background follow up - syncing up with counterparts AFTER the delegate has started communicating to see how things went and if there is anything to resolve.
(invisible) - reviewing static work as it's being done - if there are tickets, design specs, other artifacts, reading the joint work and reviewing for quality.
There's probably as many ways as there are managers ... and different managers will take different approaches based on the organization, the nature of the collaboration, and their own personal style. For example, I work in a fairly informal structure that endorses collaboration informally between teams to the point where "tell your manager you did it later" is an acceptable approach in some cases. And... I'm a pretty big loud extrovert in an industry full of quiet introverts. Because of my big mouth and obvious presence, I tend to try to counterbalance that with 1 kick off mail, plus lots of the "invisible" items on the list above. That way, my less-outgoing individual contributor can take center stage, and I can stay in the background to back him or her up.
Get the Support you Need
If you've gotten to the end of this and you think "yeah, but I rather feel like my manager drop kicked me into awkward situations and then left me no safety net", then have a talk with your manager. Bring up the places where you feel the collaboration is at risk (ie, likely to mean the work will be slow, of poor quality, or take more effort than is reasonable), and then have thoughts in mind for how to be better supported, possibly drawing from the list of support ideas above.
Try for a compromise that takes a minimum of managerial effort - it seems like your manager ought to have time for it, but if you thought about the tradeoff between "spend the time it takes to manage the inter-org communication" vs. "spend the same time putting together a proposal for raises for everyone" - would you feel the same way?