I probably should stay clear of this topic; I usually don't post on topics relating to outdated and unsupported versions of J! but I would like to offer a few observations.
Before this topic is completely derailed with a he-says-she-says debate, there is nothing essentially wrong
with using outdated, unsupported software to operate a website. It's a matter of personal choice. Further, if the website continues to provide benefits to the site owner and their customers, who are we to dispute this?
There's also nothing basically wrong with using outdated, unsupported versions of PHP—to the extent that the webhosting provider continues to make such software available—but it's purely a business decision for webhosting providers to continue providing outdated software for their customers.
There is also nothing essentially wrong with the article—written five years ago—except that the article was written five years ago and a lot changes in that length of time. At the time the article was written, the suggestion that "[one does] not have to upgrade your Joomla installation to 3.x if you don’t want to"" is reasonable, I suppose. One does not have to do anything if one does not want to. I don't have to comment on this discussion but, for what it's worth, I'm doing so, anyway.
Some technical discussion forums offer better advice than others, especially when it comes to advising people about how to continue to use outdated, unsupported software. People are free to choose where they obtain advice.
I don't use J! 2.5 (or previous versions of J!) and I haven't used them for a lot longer than five years. It's just not something I'm interested in doing. However, I am concerned about the way that some people—those who continue to use outdated versions of J!—are often treated by members of this forum community. Although the conventional wisdom is to not use J! 2.5, it's not our job to pressure people into doing something that they're (a) not willing to do, (b) unprepared for, or (c) not interested in doing.
Getting back to the original problem about caching: if caching is a problem then don't use it. The benefits of server side caching are minimal but the problems they cause may outweigh those benefits. I would suggest searching Google for "To cache or not to cache?" and see what other commentators have to say in this regard.