In fact I think this should be standard of the PhD curriculum.

In the first year you are clueless anyway, what a better use of your time than replicating some established result, and then publish your findings. In the experimental world the author will often skip details that are crucial to the success, just because it has become second nature to them. A replication study will reveal these, aka you know you need really sterile room to make this work, or you need to set-up this way your linux distribution.

PhD programmes usually require by definition that you discover "new" stuff. The difference between a bachelors/master's thesis and a PhD thesis is almost exactly that. Unfortunately reproducing doesn't tend to count, and even then if you reproduce a bunch of stuff just to find that it works, you haven't done anything novel.

In order to get a PhD out of it, you'd likely need to do a large number of reproducibility work, specifically going off some hypothesis like "method X has failings due to Y" and then testing it by doing the reproduction or similar. This makes it not low hanging fruit. In addition reproducing work is often very hard and time-consuming as you discover just how much is left out of papers/SI/appendicies.

At the time when they need to be making connections and needing patronage you want PhD students to be showing up integrity and honesty problems and asking awkward questions about the powerful people in the community?

Of course that's what should be happening, but the incentives aren't pushing in the right direction for it currently.

At least in the US you cannot base your PhD on it. It is already done sometimes to validate your own lab setup.