Government funding of science and a proposal/grant system. Senior people spend a lot of time writing proposals, and need underlings to do the leg work. They also have to be politically savvy so their peers don't reject their proposals.

To expand on this, before World War II, there was far less federal funding for science, and I don't think university faculty had the need to bring in external funding that they do now. I don't know the history of requirements that faculty bring in funding, however.

https://www.ncbi.nlm.nih.gov/books/NBK45556/

By that point most of the low-hanging scientific "fruit" had already been picked. Due to increasing complexity and the high workload of running experiments, solo scientists could no longer make much progress. So they had to act as administrators and project managers, leading larger teams of assistants and graduate students.