I find it strange that most US departments have so little transparency in tenure-track jobs searches. In the UK the system is a little cleaner. Jobs are generally announced in one place (jobs.ac.uk) and the interview date is often set in advance. In the US there is no central list of jobs and it is difficult to determine where in the process the search is. Why don't search committees set a date for the short list to be decided at the outset and make it publicly available? Even for searches that move sequentially through the short list inviting candidates one at a time for interviews, could still send out a notification. It seems it would reduce the stress of the search for many applicants and not be too much work for the search committee.
There are several factors at work here:
Remember that there are several thousand colleges and universities in the United States. A central database of such jobs would be significantly harder to publicize and organize.
Most universities in the US are private. They are under no such compulsion to post their jobs on any particular web site, unless constrained to do so by the funding sources that are supporting a particular position, or legal requirements to do so. (To my knowledge, there is no such requirement.)
The more deadlines and constraints you build into the cycle, the more pressure you put everyone under—applicants, recommendation writers, support staff, and departmental faculty involved in the search.
So I think there are multiple reasons not to publicize the results of a search, and I think most hiring committees would be reluctant to do so. There could be a better job done of announcing searches, certainly, and that would make things easier (but again, the places that currently advertise would likely complain about losing their business to a central source!).
In math, jobs in the US are announced on mathjobs.org, and you apply centrally through this website as well. Although you don't always get notified on the status of your application, we have a place called "mathjobs wiki", where people post "rumors" (in reality, since the TT interviews are announced on the department websites, it's not really a rumor) on the status of the job search. I am told that several other disciplines have something like this.
I would have thought European searches have less transparency; it seems to me that many European (mathematics) departments hire based on who you know, and their jobs are much less advertised.
I will tackle the ``Jobs are generally announced in one place (jobs.ac.uk)'' part. As user14449 mentioned in his(her?)(its?) answer some disciplines have society run central job boards. The AMS and MLA are the particularly effective ones from my experience but even they do not attract all the jobs in their fields. Then each state university will post all of its jobs to their own Human Resources job board. But there will never be a centralized site like jobs.ac.uk because the US system is not a single system. many of the colleges and universities are privately run, the rest are run by the state governments, and four run by the military. There is no central authority that can determine how hiring is done beyond anti-discrimination and equal opportunity laws. So any such website would have to start off as a third party endeavor. And since the job ads in the Chronicle of Higher Education already service this purpose but do not cover the entire market it is hard to say that there would be promise for any new one.
Just a side note on the scale of the US job market from Wiki there are ``4,495 Title IV-eligible'' colleges and universities. Title IV-eligible means students at those institutions are eligible for federally backed student loans.