What is the point of journals nowadays? I'm not sure if this question is too broad or opinion-based, but I have been wondering about it for sometime.

In the old days when communication was not as abundant as is today, periodicals were a very effective means of communicating one's research and findings to interested people. Books and personal letters were also available, but were either not suitable for short communications or narrowly accessible. Thus, journals made sense at that time.

Today, however, especially with the widespread use of the internet, I find it hard to justify the existence of journals other than to preserve the status quo from the past. In fact, I can see several disadvantages such as:


Economic burden on institutions and individuals.
Unnecessary delay in publication due to processing and reviewing times.
Subjective editor/peer-review process with many decisions made based on personal and/or journal-specific reasons.


So my question is: are there any real advantages of having journals nowadays? Wouldn't it be better to adopt an open publication method (maybe similar to that here at SX) in which people can rank, cite, and vote on publications instead?
The primary reasons for the continuation of academic journals are correlaries to some of the things you've mentioned as negative. 


Peer review. This a key driver for academic publishing in general. It provides a way to control the quality of published material, and an enforcement of accepted standards, and (for the author) feedback prior to publication. 
Communication. Journals provide a means of communicating research to a targeted audience. Conventional subscription-based models do so for a fee, while the rapidly growing open-access model (which I highly commend) provides even broader and easier access for researchers, students, and others. 


In short, journals serve to curate content to meet the needs of a particular audience, and thus they are unlikely to completely disappear in the near future.