I also have a rotozip that’s a bit worn from construction work, and it’s about as loud at no load as my bosch colt router. Not sure if rotozip made other models or if yours is somehow different than what I have. Either way, usually it’s the noise from the bit cutting that will likely dominate the environment by a large margin.
So like you could get a watercooled spindle, which will run almost silent at no load, but as soon as you start cutting wood or metal with it the bit will sing away. I think an enclosure is a great idea, but as Oliver mentioned visibility is important, and a see through door isn’t easy for most to build/maintain. You might use lexan or tempered glass for safety, but it will probably need to be heavy and dual pain to trap noise. The whole enclosure will have to be heavy for that matter.
The subject of soundproofing garages has come up here before as well. If I started having issues with noise, I would probably just spend a Saturday building a small double drywalled room in my garage for it. Then it would be safer when operating laser cutters since the drywall would contain fire from spreading to a garage (normally with lots of flammable liquids stored nearby). It would also be easy to make a very effective ventilation/dust collection setup for it, with cross flow and all. Doesn’t have to destroy the garage finish either… just don’t tape the corners of drywall where it meets your garage wall, then you only have framing nails to patch and anchors to grind off if you sell your home.