Journals

If journals are becoming so expensive, why can't the bigwigs of any area of research set up a website and then publish online with open access? You get to read all the others' data almost as soon as they get it analysed, and your work gets seen by everyone who matters.
So what is the flip side to this except for Elsevier? Or am I being naive?
Another aspect-
For a person not working in any Instt., getting to read a paper is really difficult. Nowadays, this is not of much interest to me, but 20 years back, it was a big contributing factor to why my career in science got aborted. However, in the interest of women or men who choose to take a break, it is essential to be able to keep in touch with what's happening (in between nappy changes for example).
Why cannot an IIX/University , allow membership and online access to its libraries for any of its alumni on the payment of an affordable fee? (remember the person is unemployed- so affordable has to be really inexpensive).

BTW, one of my ex students is working for her PhD in the XXX University and she says she can access only free online journals and I know that the Departments at the University do not have many print journals after the 1970's . So how do they get their lit. survey done? Is this the norm in all universities?
An article reminded me of the travails of paper chase in the 70's.......one goes from Own lib to INSDOC to DGHS ....to any place likely to have the journal one needs....
There is a law that says...if in the third library 20 km and 2 hour bus ride away, you find the right journal, right issue, the chances of the required page being torn away is 95.5%
The top floor of the IISc library had amazing journals...from the mid 19th century.