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I've never heard of any issues with monolights. The 'nasty bits' are pretty well shielded from users. But, with pack and head systems, worn or damaged head cables and connectors can be a shock/fire hazard.
The main hazard from big strobes is probably flying glass from an exploding flash tube. Most big studio units can be equipped with a glass dome or other protective shield that that covers the flash tube and modeling light. This is useful when you have a "bare" reflector close to, and aimed directly at, a subject. This is mainly an issue with higher power systems, but even low power monolights from Profoto have built-in glass shields, and Elinchrom sells optional glass domes for theirs.
Sports shooters who put big strobes overhead in basketball arenas, etc, usually put (ventilated) clear lexan safety shields over their reflectors to protect the players and fans from possible falling/flying glass.