I think weight reduction is the main reason. Reciprocating masses upset dynamic balance, thump thump, and accelerating excess weight is wasted work. Best to reduce both effects by removing metal that doesn't contribute to strength.
A double acting steam engine conrod in tension need only be thick enough to take pull forces because there's no tendency to buckle. In compression, pushing, the same conrod has to be strong enough to prevent buckling. Compressed rods are weakest at the centre point and least likely to buckle at the ends. So it makes sense to size the ends small for tension and the middle big to resist buckling forces.
Simple tapering seems most evident on big stationary steam engines probably because their conrods are relatively long thin affairs. Locomotive conrods are comparatively stubby but heavy, and their geometry may favour flatter conrods, in which case girder forms and weight reducing holes may be easier to make and stronger than a taper. IC engines are even stubbier. As smooth curves are good at reducing fatigue, I'd guess conrod design uses several ways of reducing weight whilst managing stress. Be interesting to FEM model a few different designs to see what the pretty colours say.
Dave
Edited By SillyOldDuffer on 14/07/2020 15:02:48