Performance Road Flat Shoe/Pedal combo
The shoes and pedals that are appropriate for road cycling are the ones you feel comfortable using.

Almost all MTB shoes come with a "plug" over the screw-hole recess that you could just leave in place. Make sure that's the case with any pair she has her eye on, if she decides to go that route. These probably won't be ideal, as they're still designed to work with cleats, so there won't be a natural interface surface. Many MTB shoes are identical to road shoes except for the cleat attachments and the greebling on the sole.

If she wants to stick with flat pedals and no toeclips, look at downhiller pedals, which typically have a big open platform with studs for grip. If she is open to toeclips, there are platform pedals meant to be used with toeclips (mostly targeting commuters), so you get good support for flat shoes.

There are shoes meant to be used with DH pedals, that pretty much look like standard sneakers with flat soles. This will fail the "sleek" test.

AFAIK, there aren't a lot of straight-up road shoes not designed to be worn with cleats. They'll have hard, slick soles that will be a downright hazard on flat pedals. You might have some luck searching for bike touring shoes. That's a category of shoe we don't see much of anymore, but when they were popular, they had road-shoe styling with flat soles. There are still some throwbacks to that style if you look for them.