This is the sort of thing I mean:

Oh, dear, I forgot how to post pics, it's been so long. Another try:

There is this, from Nutone that is indicated for removing cooking odors and steam from kitchens but that it is Not to be mounted over cooktops.

There was a company that made decorative antique looking ones that had the same disclaimer that they were for room ventilation but not over cooktops, but they went out of business.

The old versions of these used to come with a round grease filter. The other thing is that I don't know where you live but the older versions of this let a lot of cold air in, too.

Here is a link that might be useful: Nutone

I think you can get a metal cover for those I am not sure, but why doesn't she consider something like this?
They are essentially concealed on the underside of the cabinet. I used one here:

My parents have a pop-up or hideaway hood that turns on when they pull the cabinet forward. I know that Miele also makes them.
{{!gwi}}

Here is a link that might be useful: pull-out range hood

Last year I looked for a good one like they had in the old days and came up empty.