The TECH article says that there is still no known resolution but whilst this could be out of date the 7.1 release notes do not specify that this issue has been fixed. I haven't got 7.1 installed so I can't confirm but it doesn't look like this has been fixed.
This feature does have some value if you are working in an environment with large volumes being handled by a relatively large team with limited responsibility e.g. a call centre churning out tickets. Rather than having them hunt around for tickets it makes sense to provide a feature that takes them to oldest task that needs to be dealt with.
However in practical situations this doesn't really have any value and I agree it would be very nice to turn it off :)
Although something to note, the countdown only appears on tickets which you open from the find ticket or open ticket web-parts. If you open a ticket by clicking on a link or from a report for example then it isn't displayed. So this means that you can work-around this to some degree by providing users with a report that displays details of all their tickets and allowing them to click the process ID to open their ticket.