I wrapped all my fiberglass traps with a super thin layer of plastic drop-cloth...about as thin as plastic food wrap...which has no significant effect on audio passing through it, but guarantees that no glass fibers will ever get out...though it was probably overkill, since the fiberglass panels were aluminum/paper covered on one face and wood covered on the sides/tops...plus polyester felt covered on both faces...and finally acoustic cloth covered on both faces as the final layer.
Considering that these are very large/deep traps that are multi-use "mobile" and not permanently installed...I just wanted the extra insurance that the fiberglass would be sealed.
For permanent mounting on walls, I think fibers escaping is not a real concern. On ceilings....mmm....I think I would want to seal them.
I think very well thought out and my concerns exactly but on some of the videos on the subject there is no specification to the material that is used.
I would prefer more natural types of insulation and enquired about such when purchasing it but it is so incredibly expensive compared to fibreglass types.
The sheeps wool stuff really confuses me as wool has no value (ask any sheep farmer) but sheeps wool insulation will break the bank. Anyway I would rip my skin off so it is foam, moveable Rockwool panels and an experiment with old towels when they arrive.