Has increased polarization forced presidents to be more proactive setting the legislative agenda — or, at the very least, forced presidents to take a public stand on more issues?I'd be willing to bet that the answer here is no -- that the culprit in any increase over time would be the modern presidential nominations system, not polarization. Pre-1972, candidates could campaign for the nomination without necessarily having to give a whole lot of targeted stump speeches to a wide variety of differing audiences, or to appear in a series of pre-nomination debates. Even those candidates who did contest primaries, such as John Kennedy in 1960, only entered a handful of those races. In the other states (and in some primary states as well) the campaign for the nomination was not fought mainly over delegate selection; it was a fight over convincing already-chosen delegates, many of whom were supporters of a fairly small number of delegation leaders, to convince those delegates to give their support to a candidate.
Both systems require plenty of promises and back-room deals, but the current system forces a good deal of those promises and deals to become part of the public record. I'd be surprised if this doesn't lead to a lot more detailed promises during the campaign, which in turn leads to more of an incentive to act in the Oval Office.
The argument on polarization would presumably be that given the lack of internal differences within parties, it's less risky for a candidate for the nomination to stake out positions. But that presumes that nomination battles are public contests in the first place -- which gets back to McGovern-Fraser (that is, reforms of the nomination process before 1972).
However, I don't recall seeing any study on the issue, so it's mostly speculation on my part.