This question is somewhat vaguely structured. But, I hope someone can make it more precise (or) it is indeed possible to answer it in the form that I am stating it.

**Background** : I recently chanced upon the following lecture note of Langlands : http://publications.ias.edu/rpl/paper/2578 . In this, he has various comments/proposals on geometrical approaches to aspects of the Langlands program. I don't understand several things about it but the following question came to my mind.

**Qn** : *If you are Beilinson-Drinfeld in the early 90s looking to formulate a version of Geometric Langlands. Why are moduli spaces of stable Higgs bundles (arising in Hitchin systems) on Riemann surfaces the right place to look at and not just moduli spaces of stable vector bundles on Riemann surfaces ?*

(the connection to the Lecture note linked above is that Langlands discusses the theory of stable vector bundles, especially the work of Harder-Narasimhan, Atiyah-Bott etc and provides certain conjectures in the language of this theory. )

PS : There is actually a 'physics answer' that I can think of. As is well known, Atiyah-Bott were studying two dimensional Yang-Mills (gauge) theories. Such theories do not have an electric magnetic duality relating the theory for $G$ and the theory for $G^\vee$. However, such dualities can occur in four dimensional gauge theory. The most robust such duality is for the maximally symmetric $\mathcal{N}=4$ Supersymmetric Yang Mills theory in four dimensions. And in the gauge theory approach of Kapustin-Witten to the Geometric Langlands Program, this electric magnetic duality is indeed the starting point for obtaining statements about geometric Langlands. When you compactify the four dimensional theory on a Riemann surface, one naturally obtains Hitchin system(s) from the physics (I am being telegraphic here, omitting details about twists, defects etc). Plenty of MO threads do a better job of this. But, the point is that if a 4d field theory (more accurately, a TQFT built from it) is the starting point, then the Hitchin system is what one gets naturally. But, I suspect there might be another answer since Beilinson-Drinfeld's original approach was not motivated by dualities in four dimensional field theories. Hence the question.