Transactional leadership is based in contingency, in that reward or punishment is contingent upon performance.
Despite much research that highlights its limitations, Transactional Leadership is still a popular approach with many managers. Indeed, in the Leadership vs. Management spectrum, it is very much towards the management end of the scale.
The main limitation is the assumption of 'rational man', a person who is largely motivated by money and simple reward, and hence whose behavior is predictable. The underlying psychology is Behaviorism, including the Classical Conditioning of Pavlov and Skinner's Operant Conditioning. These theories are largely based on controlled laboratory experiments (often with animals) and ignore complex emotional factors and social values.
In practice, there is sufficient truth in Behaviorism to sustain Transactional approaches. This is reinforced by the supply-and-demand situation of much employment, coupled with the effects of deeper needs, as in Maslow's Hierarchy. When the demand for a skill outstrips the supply, then Transactional Leadership often is insufficient, and other approaches are more effective.