I don't really think this is an owner's vs the players issue at all. I doubt there's any disagreement between the parties on this matter. It's that third party they worry about, their bosses, the consumers. And that's a dwindling audience. MLB is doing better about getting people into the ballparks, but the pie is shrinking. The DH would seem like a slam shut case, but don't piss off the purists.
They can't mask the dwindling baseball audience forever, they've already tapped into the big revenue stream with TV that's enabled the growth of payrolls across the league and the branding of ballparks. But are those deals going to be worth as much when the audience keeps disappearing? I'm just old enough to remember when most every kid could name every team's lineup. Now, a lot of that had to do with the baseball card speculation boom, but there was a time before Selig when kids talked about baseball between classes. There was a time when kids actually played baseball! Now the soccer fields reside the diamond graves.
We could take this all to the natural extremes, but where is the line drawn? The designated hitter is counter to the very spirit of baseball, which is that everyone is a two-way player. It's those little things that are the very difference between a major leaguer and a career minor leaguer. Where do you draw the line? Why don't we go back to a 154 game season, eliminate extra inning games by introducing ties, no more doubleheaders, no more day games in the blistering sun, how about two DHs? You could have an offense and a defense like in football. Those are extreme outcomes, but when does it make you turn away?