While the notion of getting realistic simulated motion for character-attached objects is theoretically appealing, things can quickly get quite dicey when you consider that character animations/movement are often way beyond “real world” speeds, which can lead to lots of hairy physics interaction issues. There are obvious cases of characters whose movement is intended to be super-human (think things like “dash”, or double-jumping), but even things that are just tuned to feel responsive for game-feel purposes are often incredibly abrupt and rapid (in-place turn speed, etc.).
This is something nearly everyone has to deal with for things like cloth simulation, where you sometimes just freeze the simulation (or put it into a keyframed state) or do other hacks to prevent it from freaking out due to intense accelerations or body movements. Similarly, using rigid-body physics with constraints can be troublesome too; you can end up needing several spring constraints, etc., just to keep things behaving themselves. If the attached object is intended to interact with body-accurate collision, then you also have the fun of considering what the body parts are supposed to do in response. If they are keyframed, then you now have basically infinite mass body parts moving at incredible speeds hitting (and causing collision response on) dynamic low-mass rigid bodies. In one particular title I worked on, taking out of account cloth and attached objects, just the body-accurate collision interacting with world dynamic objects was so problematic (turning in a pile of boxes causing them to essentially explode outward) that I had to damp/zero the velocity of objects colliding with the body to prevent the character from being a debris launcher.
All that said, it can be done, and I myself have done it in very targeted cases in the past. But I would caution that expecting this to work well in the general case, even for characters that are animated “realistically” and move at semi-sane speeds, is probably overly-optimistic. I also tend to lean in the direction of not having systems quite so reactive/inter-dependent, such that doing something as innocuous as tuning the run speed will have all sorts of knock-on effects on simulation. But things like you mention can be done, just more explicitly ("oh, character just was near an explosion of X magnitude, detach, make dynamic and apply appropriate force").
