As others have alluded, the Osaka-Kyoto split is a little problematic. You could certainly do it that way but it complicates your travel a bit. On the JR Haruka from KIX, it is only another 30 minutes or so to continue on from Osaka to Kyoto. When traveling into KIX, I prefer to just go all the way to Kyoto and leave Osaka for day visits. That way, I don't have to do a hotel move with luggage in the middle of my Kansai stay. The Haruka has plenty of luggage space.

The best reason to include an Osaka stay in your itinerary would be if you are nightlife people and want to immerse yourselves in the Osaka nightlife and restaurant scene. A few of our regular posters do just that and are very happy with it. I tend to nest up in my hotel for the evening quite early and spend my time getting out early in the morning and seeing things during the day. In that case, it just makes more sense to stay in one hotel and use the extensive train system to see other, nearby cities. YMMV.

The shinkansen makes little sense between Osaka and Kyoto since the trip is so short. The Haruka would be a "high-end" option from Shin-Osaka or Tennoji Station to Kyoto but the local trains would be a lot cheaper. See Railroadtycoon's post above.

JR