It's little coincidence that the last of these facilities is housed in Utah. The Church of Jesus Christ of Latter-Day Saints contributes a significant amount to family history work, which includes reading and deciphering old records written mostly in cursive. They also encourage their members to contribute to this work. Around half of Utah's population are members of that church, so there naturally is a much larger pool of qualified cursive readers to select from there.
Not sure if this remains true today, but back when I was young you could go to your local LDS church and use their computers to search genealogical records. It may not be as useful today, but in the 80s it was some of the best stuff you could easily access.
So there are still FamilySearch center in many meetinghouses of the Church of Jesus Christ of Latter-day Saints. They have also put almost all their records online at www.familysearch.org
If you go to the meetinghouses however you can also get access to the records of several other organizations that have partnered with FamilySearch for reciprocal resource sharing.
