[jacquesm]

Sure, so you hit all of the people that have all of the pieces. Problem solved.

[saalweachter]

Or you publicly announce you're hitting 1 of the N people with the rubber hose until M-1 of the other people send you their key fragments.

It's not like these keys are shared among disinterested strangers who have no attachment to each other.

[worthless-trash]

Somehow, somewhere you've just influenced a megacorp's internal crypto process.