My experience with this has been variable.

I think it's best to set your HH profile to earning the 750 points.

Sometimes you need to leave before 6am on a one-night stay; so you can't have breakfast and obviously points are better than nothing.

Sometimes you book a rate with breakfast included, or breakfast is free for all guests, so you might as well get the points too.

Sometimes they ask you at check-in to choose breakfast or points. If you choose breakfast they give you a breakfast voucher. But if your profile is set to points, when the stay credits, you get the points too.

The last possibility is that they notice your profile is set to points on check-in, and decline to give you the breakfast. Then you ask them to change your preference. Sometimes, the change does not propagate to Hilton properly, so again you end up with both breakfast and points.