If you have a fixed number of resources, then the only way the team can take on a large new story is by not doing an equivalent amount of previously-assigned work. If the team is honestly working as well as they can, then even small tasks cannot be taken on without other tasks slipping. If they are lazy so-an-sos, or have been withholding effort from you then they can absorb more work.
So why is is that when a team can absorb more work without letting anything slip they get rewarded, and when they cannot they are criticized? Doesn't it seem like they should be given credit for really working at capacity all the time?
Or maybe it's a wise leader who quietly keeps a small reserve so that he can respond quickly to new requests. Should I, as a manager, keep one or two people working on easily-interruptable, low-value activities so that I can respond when the emergency of the day comes along?
There are clearly advantages to both. I've been running fully-committed for a while and there is almost always some kind of emergency or special project that needs tending at some point in the week. It is always "very important." I suppose a wiser fellow would keep some developers in reserve.
OTOH I would not be able to look anyone in the eye and say we were 100% engaged if we weren't. I could phrase it cleverly as "I can't afford to put any more man power into this", but that is a cop-out. Say I hold my reserve and nothing happens -- then I actually prevented the team from delivering value, which seems obscene. Or if I hold the reserve, and something comes up; won't it seem odd that there were no available horses for task A but there are for task B? Clever phrasing is not truth. I'm just not a "convenient distortion" kind of guy. I value a clean conscience. I want to work in a transparent shop, so I have to maintain transparency.
I will keep people fully engaged in the most sustainable way possible, and be sure that each new "hot case" or "emergency" has a known opportunity cost. When someone says "this has to be done by Tuesday" then I must always follow with "Okay, which of these equal-or-greater sized tasks can afford to slip?" If nothing can slip, then clearly the case is not so hot or the emergency not so urgent. Maybe the stake holders can fight over it long enough for the developers to free up.
I am not going to sacrifice integrity here. I guess that means I should be ready to deal with the criticism when I have to push back for someone to make a priority decision. Nobody said a clean conscience was without cost.