There are a few different reasons why I think this.
1. Ohio State does not draw very well for a school of its stature. If they are playing more games against Minnesota, Wisconsin and Penn State, that should bring in more casual fans who may not normally pay attention to hockey. While this may be true w/any Big Ten School, Minnesota, Wisconsin and Michigan don't really have issues as it is currently selling tickets. If Ohio State is able to sell more tickets, then one would generally assume that they will be making more revenue, which they could then put back into the program via better assistants, more money for recruiting trips....which leads to
2. Ohio State should be able to recruit better. Again, Minnesota, Wisconsin and Michigan (I do not intend to leave MSU out of this, it's just that I know much more about these three programs, so I use them. Please do not feel slighted.) basically don't have any issues currently with recruiting. For the most part, they get who they want. Ohio State doesn't. The Big Ten will definitely give more publicity to an Ohio State hockey program, and it would make sense that solid kids who may have turned to a different school, would now turn to Ohio State as an elite option. I'm not saying that Ohio State would be #1 in recruiting (everyone knows that is Michigan), but even if they are a top 10-15 that would be a jump from where they are now. If you have more solid recruits that leads to...
3. Ohio State should then win more games. While it may not be 30+ win seasons, it would be reasonable to assume ~20 wins. Of course, if Ohio State is better, and winning more games, that comes at the expense of the other Big Ten Teams. If they are able to string together solid seasons, make a few NCAA Tournament games, get better recruits it will lead to more attendance, more revenue, better (or at least better equipped) assistants for recruiting trips, which leads to better recruits, and more winning. It is a cycle which ultimately puts Ohio State as a top 15-20 program in the country. They most likely will never dominate like Minnesota, Wisconsin and Michigan, but they will find their niche in the conference, and "steal" wins from the Gophers, Badgers and Wolverines.
At the end of the day, if you have a program that can sustain itself financially, it has a significantly greater chance for success. Do you ever wonder why Minnesota, Wisconsin, Michigan, North Dakota, Denver, Boston College, Boston University, New Hampshire...etc are always in the hunt? It is because they have invested the most into their programs. Ohio State, by percentage, will most likely increase their commitment to college hockey more than any other school in the Big Ten, with the exception of Penn State.
Obviously this is not a sure thing, but I never said it was. All I said was that Ohio State has the most to gain, and this was my reasoning why. I'm sure there are other valid points as well that could support my argument.