Is a good PhD student or researcher expected to spend some part of their day/week regularly reading new research papers/pre-prints? Or alternatively do good PhD students and researchers spend some part of their day, regularly, reading new research papers and pre-prints?
Please give some reasoning of why and why not, if possible.
Background for those who are interested:
I am a physics student. I am new to publishing research papers and research in general. Just around a week back my summer intern work was submitted to a journal and a pre-print was made public in arXiv (I am the corresponding author). This was my first experience with publishing a paper, so I didn't know what to expect (except for corrections, major/minor revision notification from the journal ;[ )
However, within 12 hours of being public in arXiv, I received a mail from a PhD student and the next day I received a mail from another PhD student. One of the mails was about how his research paper (published a month back) disproved a popular notion which we had mentioned in our discussion and the second one about his research paper and possibility of matching both our results.
Both of these PhD students were from two very very prestigious universities, so I was quite surprised. While I expected people asking for clarification or pointing out mistakes I did not expect such a practice.
Is it common for all PhD students to do this? Or do good researchers do this on their own? (Which might explain why these two are in top schools). But the topic of this research is very hot with lots of new papers being published every week. So I can't imagine how one would achieve it. Also, until now, I always thought that we will have a specific problem for our PhD, so I am not sure in what way this'll be useful. (I know one has to do literature study before starting.)
Since I would be applying for graduate schools next year I though this might be something I should practice, if it helps me as a researcher.
There are pages like http://www.arxiv-sanity.com/ to filter the mass of papers on arXiv and give you the chance to read what interests you most. Furthermore, you can also go through all recent papers on your phone (instead of browsing instagram, reddit or whatever), read the abstract and mark everything that might be interesting to later read. I'm not sure if it is expected, that might strongly depend on your institute, group or advisor, but it is surely possible to do it in nicer ways than by simply clicking through arXiv directly.

I know good researchers who check arXiv daily, I know other just as good ones that haven't looked at it in months, so there also is no general rule there for after the PhD it seems.

Btw, if anyone knows of other nice ways to filter the arXiv feed, feel free to share/add, I'm not yet 100% happy with the ones mentioned that I currently know.