Big giant NO.

Wall as in dry wall to cover your hood? Aesthetically I would not care for that at all. Cleaning dry wall above a cooktop? No to that one as well. If you don't like to see the hood, why not cover it with cabinetry? with faux doors?

Instead of putting a wall in front of the hood, you’d need a hood insert to achieve something like in the pics below.

Thank you for confirming my concern. I like the hood insert idea. Any suggestions on a good 36" insert? My appliance guy sent over the Zephyr Monsoon but it only goes up to 715CFM and we are not impressed with Zephyr in another house. We are either going with a Wolf or BlueStar 30" range so we are thinking of something 900CFM or above. What about Zline? It goes up to 1200CFM and is less than half the price of the Zephyr.

My suggestion is to look at an external blower motor with an inline silencer. We started with a Zephyr Monsoon but found it so impossibly loud that we bit the financial bullet and did a do-over. The 1400 cfm roof-mounted Abbaka blower is quieter on high than the Zephyr was on low (according to the admittedly imprecise decibel meter I downloaded to my phone), and the knob control of the Wolf liner is much nicer than pre-set buttons for fan speed.