Simultaneous Equations Models (SEMs), together with the treatment of measurement error, lie at the historical foundation of Econometrics as a discipline.
The idea of SEM’s for the economy came from Jan Tinbergen, who estimated a 24-equation system for the Dutch economy in 1936. See Tinbergen (1959, pp.37-84) for an English translation. When the first Nobel Prize in Economic Science was awarded in 1969, Tinbergen shared the inaugural honour with Ragnar Frisch (a Norwegian econometrician) for their pioneering work that led to the development of econometrics as a recognized sub-discipline.
It's not that long ago that courses in econometrics included a solid amount of material relating to SEMs. Consequently, students became well aware of issues surrounding parametric identification. They were also very familiar with a raft of estimators designed to deliver consistent, and perhaps asymptotically efficient, estimates in the context of simultaneous systems. These included single equation estimators - generally Instrumental Variables (IV) estimators such as 2SLS and the k-class family, including the Limited Information Maximum Likelihood (LIML) estimator; and full system estimators such as 3SLS and Full Information Maximum Likelihood (FIML).
These days, the estimation of SEMs seems to get relatively little attention in standard econometrics courses. Most students learn about 2SLS, and many of them appreciate that this is just a specific member of the IV family of estimators. However, few students realize that all of the other estimators - yes, including FIML - are also in the IV family. For example, see Hendry (1976).