Reading about some of the grand Allied offensives of Joffre and Haig on the Western Front during WWI, I'm struck by how the infantry breakthrough would be followed by a massive cavalry sweep to exploit it, which did not work. Did cavalry use make strategic sense, or was high command naive?

In large part, you are correct. The coordination and execution of a massed cavalry attack to achieve breakthroughs was unfeasible on the Western Front once the frontline settled.

I will be looking at this from the perspective of the British cavalry, but many aspects to be discussed applied to the French cavalry as well.

A principal reason that the cavalry could not achieve and sustain a breakthrough lies in communication; it was very difficult to direct any cavalry towards a gap in the frontlines before it had been sealed. The communication methods used to relay information between the frontlines and staffers did not exactly lend themselves to speed. Pages 192-196 of John Keegan's The First World War describes this problem in detail. The lengthy process of communication compounded the problem of directing cavalry against a potential breakthrough.

The horses' vulnerability to artillery, barbed wire, and the moonlike landscape of No Man's land also made the strategy of massed exploitation untenable. A quote from Robert Marks sums up the issues quite neatly:

While the cavalry could still be a useful mobile reserve, the horses needed to be brought up to the front lines before they could race through the gap - but with damage from enemy artillery extending kilometres behind the line, "cavalry tracks" had to be created the night before just to allow the horses to reach the attack point. Then, No-Man's land also had to be cleared of barbed wire, and cavalry tracks placed down in it - often so narrow as to cause traffic jams. Even if a gap could be created, bringing the cavaliy in to exploit it from their staging area could take upwards of an entire day, by which time the gap had been sealed.

These "cavalry tracks" were necessary because the craters that riddled the terrain of No Man's land posed a serious hazard to horses. There was little flat ground to be be found in the space between trenches.

For the British in particular, the cavalry simply was not present in great enough numbers to make any sensible difference once the war became mobile again. When Germany began Operation Michael, cavalry composed only 1.01% of the British Expeditionary Force.

So to answer your question, a variety of factors all made massive cavalry sweeps an ineffective strategy in the relatively static warfare that was present for so long on the Western Front. However, I would pose that the strategy was not entirely unfounded. The cavalry was undoubtedly the most mobile arm of each Army on the Western Front for the majority of the war, and so it follows that they would be relied upon to exploit breakthroughs.

Sources:

Bowes, Richard Lee. “Waiting for the ‘G’: A re-evaluation of the role of the British cavalry on the Western front, 1915–1918.” Master’s Diss., Royal Military College of Canada, 2000.

Marks, Robert B. “Crossing the Fire-Swept Zone: The British Cavalry's Transformation into a “Swiss Army Knife” on the Western Front of World War I.” Master’s Diss., Royal Military College of Canada, 2011.

Phillips, Gervase. “The Obsolescence of the Arme Blanche and Technological Determinism in British Military History.” War in History 9, no. 1 (2002): 39-59.