Interesting is always in the eye of the beholder but this theorem plays a crucial role in the proof of the proper base change theorem in SGA4 Exposé XVII (by P.Deligne). One wishes to prove an isomorphism between complexes and the proof is pure EGA/SGA reduction style: first reduce to complexes concentrated in a single degree, then to modules over $\mathbb{Z}/n\mathbb Z$, then to flat modules and then (by the theorem of Govorov-Lazard, which I knew solely as a theorem of Lazard) to free modules by the commutativity of $H^{i}(X_{s},-)$ with direct limits. For free modules, the result is obvious. The moral of the story to me as alawys been that whenever a functor commutes with direct limits, then it is enough to consider free modules if one wishes to prove something about flat modules.

Interesting is always in the eye of the beholder but this theorem plays a crucial role in the proof of the proper base change theorem in SGA4 Exposé XVII (by P.Deligne). One wishes to prove an isomorphism between complexes and the proof is pure EGA/SGA reduction style: first reduce to complexes concentrated in a single degree, then to modules over $\mathbb{Z}/n\mathbb Z$, then to flat modules and then (by the theorem of Govorov-Lazard, which I knew solely as a theorem of Lazard) to free modules by the commutativity of $H^{i}(X_{s},-)$ with direct limits. For free modules, the result is obvious. The moral of the story to me as always been that whenever a functor commutes with direct limits, then it is enough to consider free modules if one wishes to prove something about flat modules.