Actually, this was probably never something Cook County wanted because this feature is a revenue source for the county. I did not get any of my ancestors' records from FamilySearch Cook County collection and did not know they were available on the web site.
It appears from this article that one can order and see the document images on LDS microfilms. However, not very many LDS Family History Centers utilize a connection between the microfilm reader and a printer. In my experience, one can occasionally get a halfway decent photo of the display screen but this is very hit-or-miss. It has also been my experience that oftentimes the microfilm reproductions are not of very good quality.
As vital records go, Cook County does not charge a great sum for copies of the records for genealogical purposes. Genealogists can get hard copies via postal mail or digital copies can be immediately downloaded following the payment process. It goes without saying that one should get the best reproduction available.
What has been your experience with the Cook County records on FamilySearch? Will these changes to the policy disrupt your research?