...But even if we did, would that push us into profitability?
No, not as "profitability" is normally defined here. That brings us to the question of why does Ohio have football at all? In fact, why do any G5 schools have football? Is it because there is a huge demand for football amongst the students? Does the faculty love football? Does the town love football? Is it mandatory that all universities must offer football?
The answer to all of the above could all be arguably answered in the negative. Students seem to enjoy football a little as a part of the fall atmosphere, but most definitely don't love it, based on the fact that many leave at the half, if they come at all. Most of the faculty seem opposed to football. If the town loved football, as you point out, there are enough people in the county that every game could be a sellout, but they are not. Most universities do seem to offer some football, but many top academic schools limit it to Division III, such as MIT, Claremont, or U. Chicago. Unlike dropping to FCS, a drop all the way to Division III does save money, a lot of money. Going to FCS seems to result in a worse financial situation, and many FCS schools seem to want to move up to FBS at the first opportunity, so a drop to FCS would probably be a bad idea.
So, that brings us back to the question of why do schools play football at all, if it is a money losing proposition with few benefits? There is only one plausible answer, as far as I am concerned, and that has to do with benefits that are harder to quantify. During my lifetime, a major shift has happened. Fifty years ago, most football powers were not top schools academically. There were schools notable for academics, and schools notable for football, and the two were very rarely both present in the same place. A few schools known for academics, such as Northwestern and Vanderbilt, could be found in major football conferences, but they were the exception, not the rule.
Today, the situation is very different. Contributions have flooded into the coffers of football powers, causing massive growth in their endowments, and also resulting in a boom of new building construction, both leading to a significant change to their academic reputations. Today, most of the B1G schools are known for having excellent facilities, excellent academics, and are known as excellent research institutions. This, in my opinion, is why schools are willing to lose money on G5 football: They believe that it makes them a more credible institution, and attracts donations to their general fund, and boosts their endowment. I think it galls Ohio administrators tremendously when a wealthy Ohio alum makes a huge donation to OSU simply because, after a lifetime of being an OSU fan, they feel a closer connection to OSU than to their own school.
If the above paragraph is true, then the problem with the statement that "Ohio football operates at a huge loss" is that it doesn't account for any effect that might happen to general giving for the University. When Ohio administrators elect to make a raise in pay to football or basketball coaches, or to offer either sport at all in the first place, I presume they are factoring in their knowledge of interactions with alums and donors, and their presumed impression of what would happen to general giving in the absence of the sports. Since they have more specific knowledge than I do, I tend to defer to their decisions, unless they made some decision that appears outrageous, such as paying a coach $2m a year, or something similar. With only 5 football coaches in FBS paid less than Albin, that certainly isn't the case.