In many shuls, I see the majority of people begin putting away their tefillin when the chazan begins the full Kaddish (after U'va Letzion). To me this seems disruptive and disrespectful to the mourners saying Kaddish at the end. (Just because people don't complain, doesn't mean that it may not bother them.)
- Is that disruption/disrespect an actual concern cited in authoritative sources as leading to a recommendation/requirement not to remove the tefillin at that time?
- Are the tefillin supposed to be worn for the entire duration of Shacharit (except for Rosh Hodesh / Hol Hamo'ed and those who switch to Rav Tam, etc.)? Doesn't Shacharit end after the last Kaddish? (Nusach Ashkenaz - I think Sefarad is the same idea.) Is it proper then that people put away their tefillin before the end of davening?