My guess is in the absence of prominent Ohio State figures advocating for the school to try and get football + basketball finals held at the school every year, tOSU won't see a visibly strong relationship with the OHSAA (read: hosting football + basketball) as a priority. When it comes to the hosting arrangements: I don't claim to know much of the story, but you can't make someone dance with you. And if you have to force someone or guilt them into dancing with you, then there's no heart, shared interest or engagement in the dance for either party. Such I presume to be the case with OHSAA + Ohio State. Ohio State has a good idea of how they want to utilize their facilities in future planning, and evidently the OHSAA isn't #1 on the list.
But is it a rocky state of affairs? Probably not. There's no doubt the people from the OHSAA and Ohio State are professionals looking out for their organizations, and they likely are cordial and respectful with each other. The OHSAA understands to accept "no" for an answer.
Unless Ryan Day and Chris Holtmann start advocating and fighting for Ohio State to host OHSAA state finals in football and basketball, Ohio State doesn't have anyone in their walls calling on them to answer the bell.