Not sure why you think they're necessary. I'm guessing these are not your furnishings since this appears to be a real estate photo. I would upgrade the style of the chandy as the main ambient light put on a dimmer, and use a larger mantel mirror to double it. Then use art lights (accent lighting) over art at both sides of the fireplace with a credenza or chest below each. Plenty of table and floor lamps will cover the task lighting, These may not be your style but I'm posting for concept.

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In general, recessed lights work on a vaulted ceiling, as long as you use a lumenaire that can be angled to align perpendicular to the floor.

Whether you should have recessed lighting here is unknown from the model house pics provided. Be aware of differences between lighting (and fixtures displayed) in the model home vs what is specified in your exact project. And the type of recessed lighting that may/may not affect with insulating or venting a vaulted roof.

Slopped ceiling cans, and you would also have to make sure there is space to put them, do not put the remodel flush mounts they will shine the direction they face. but for me I do not see a call for them here.

they are used all the time.

If the slope is great, buy a recessed light for Sloped application, available everywhere.