In addition to the lack of titles, the other big historical difference why fans/media consider Ohio State a football school is simply how those 'purgatory' periods were. The years between 1968 and 2002 might not have produced national title banners, but still won plenty of conference titles (15 if Wikipedia is correct) while being in the top 10-15 teams in the country almost every single years, pumping out pro talent, etc. Even if they weren't quite winning titles, there was still plenty of other success to draw eyeballs.
By comparison, the basketball team went almost three decades (1971 to 1999) with two fantastic Jim Jackson years, two other Sweet 16 appearances, and then not a ton else that jumps off the page.
That said, I'm looking forward to Holtmann continuing to develop the roster. That stretch from 2005 to 2012 when Ohio State won 5 B1G regular season championships, 4 B1G tourney championships, was a fixture in the NCAA tourney, and stood toe-to-toe with Kansas, Kentucky, etc in heads-up matchups? Not a fluke, that's a legitimate level that Ohio State can absolutely get back to...and everything Holtmann has done since walking in the door has made me believe that he's got the coaching and recruiting acumen to get there.