Katie Bauer!

First: what is the state of your supporting infra for this stakeholder request? The 90-bajillion-percent of DS time is spent cleaning data is a direct consequence of this. If the data is shit quality or no one has ever worked with this data before, your infra will slow you down

A DS's visible hours will be much lower if they have to do a significant amount of data cleaning or infra set up. This will impact the stakeholders perceived utilization rate, so TELL THEM if this is the situation.

Second: what is the skillset of the DS team? This is partly about subject matter expertise, which has a huge impact on how quickly a DS can solve a problem, but it's also about the seniority of a particular DS.

Juniors need more help structuring work and identifying relevant datasets and techniques. Stakeholders rarely know the difference (and probably don't even know the level of a DS), so it might not occur to them that a given DS really IS spending all their time on an project

Third: the interests and morale of your team can have a big impact on how much effort they give to a stakeholder request. Stakeholders might not care if a DS feels like a project is growing their skills, or if the DS feels burnt out from always fielding urgent inbounds

But they CAN tell if a DS's heart is not in something. Interest and morale are more visible to them than the former two points, and even if they're getting what they need from a DS, they may still think a DS is not spending enough time on their work if the DS seems unengaged

Thus, DS managers should keep an eye on interest and morale. You can't always give your team the work they most want, but when the team can give energy to a project it's perceived as spending the right amount of time on it, even if the DS is spending a lot of time on other things

And fourth is the compatibility of a DS and their stakeholder. Not every pairing of personalities will work well together, and as a DS manager, you can only do so much to smooth that over.