You don’t cover a standard hood. You buy an insert and blower and then a wood hood from your cabinet company. 4/6K average. A plain stainless chimney hood is cheaper.

It's an aesthetic choice -- I would prefer it exposed, but you may like the look of it covered. Just the same way as some people want hidden integrated appliances with cabinet fronting, whereas others don't.

I have a ordinary modest 30" range. I bought an unfinished wood hood and finished it to match my cabinets. The hood came with a metal liner and recommendations of Broen vent inserts that would fit the hood. Total cost, hood, vent inset, and labor was $1000. I point this out in case you also are doing a modest kitchen. This is not a set up for a fancy professional range. You could not put the wood hood over an existing hood.

I have seen online people make hoods to cover existing hoods. These often are made without a liner and strike me as being hard to clean and possibly a fire hazard if mounted too low.