Good grief learn to read a signal. They obscure placement info because it is bad. The average applicant being ignorant and wondering "gee why did they do that is it a jolly fun old oxford custom?" leads to better outcomes for them than revealing their horse pucky placements.
UK academic and I have to disagree strongly with this one. Most likely they simply have no idea. During the last REF my dept was scrambling to answer the questions about PhD placement because no one had any records. So a series of frantic emails went out to the faculty asking if anyone knew where their PhD students from the prior 7 years had ended up. I understand the DPIR was the same.
I don't think US posters really grasp how supervisor-centric the UK PhD is. In many places (incl. my dept) applicants need to email a prospective supervisor and get their conditional agreement to work with you BEFORE you even apply. If you don't have that, your application will be rejected regardless of other merits. Obviously the department exists as an organizing entity and a provider of admin support, but it doesn't function in quite the same manner as it does for US PhD students. Quite simply, it's not seen as the dept's responsibility to get you a job, academic or otherwise. I am not saying that is a good thing, but just that this is the prevailing attitude among faculty.
As someone pointed out, up above, though, the Oxford Economics and Philosophy departments both have very clear placement information on their websites, so I don't think this can just be cast as a UK thing or even an Oxford thing. It seems to be a problem with politics at Oxford.