Why do journals have limits on the number of references?
Journals aim to publish an organized set of articles of some approximate length in an attractive format.

Journals set limits on the number of references to shape the form, format, and quality of the submitted articles.

This organization is a good thing, in terms of disseminating scientific information. Given the limited space of one article, there is definitely some appropriate range for the number of essential and useful references that relate to the presented work.

This is less restrictive that it might sound, as these rules set by the journal are seldom hard limits. If you have good reason to include a couple of extra references, you can usually work with the editor to get them included.

Another reason to include limits is to try to encourage authors to examine references more closely, and to be more selective in their choices of what to include. Just as many journals have rules against gratuitous figures and tables (e.g. all figs must be referenced in the text), these limits are meant to discourage gratuitous inclusion of references that are not directly related to the discussion in the manuscript.



In response to the expanded question: "What happened in the 80's?" ...

The Science Citation Index was launched in 1964. With its growth and success, and the addition of other field-specific indices, it became possible to compute statistical journal and author comparisons (e.g. Impact Factor). This concerted effort to index citations made being cited in the work of others more important, and the use of numerous citations became much more common. The benefits of these author and journal metrics were much lauded during the 70's and 80's, but people were also increasingly aware that this arrangement was vulnerable to abuse, i.e. gaming the system by inflating citations. SCI grew to become Web of Knowledge, then Web of Science and along the way (1992) it was acquired by a large media company and today it's run by Thomson-Reuters.

The question posed invites speculation; we can't know exactly what the owners and editors of the various scientific journals were thinking when they started implementing citation limits. However, I would hazard a guess that they realized gratuitous citations might be an issue, probably had a few bad apples, and decided that limits were a good idea to keep the quality of the submissions high.