when i read (present tense, having read it multiple times in my 12 yrs as a Muslim, alhamdulAllah) it, i see two things to take from it:

1) The Prophet salalahi alahi wa salaam, the best example to us and who men should strive to emulate, did these things. The greatest man was not too proud to mend his shoes, sew his clothes etc.

2) “like one of you does in his house” implies that this was NORMAL for men to do

i.e., the point of the hadith at the time was to point out that even the greatest of mankind, who perhaps could have used any number of excuses to not do so, did these common normal activities and did not place himself above other men, AND that it was a normal/common/acceptable thing for men to do this sort of work.

AlhamdulAllah…