Is publishing papers with many co-authors detrimental to one's academic career? I’m looking at some friends’ works, at good labs, in good schools, but some of their publications have 10 co-authors – I even found one with 15 co-authors.

I’m sure the lab and its PI(s) are doing well from such collaborative efforts, but at the individual level, are the PhD students being harmed, because the authorship is spread among so many people?  I wonder if this kills their chances of securing post-docs later on, because they published with a big team of people, and I wonder if this signals that they have not done enough ‘independent’ work.

FWIW, those papers are in medical machine learning.
As mentioned in comments, the normal number of authors on a paper depends heavily on the field.

The issue with getting a postdoc is that you need to demonstrate your ability to do research. That doesn't necessarily mean you need to be the PI, as in some fields as a postdoc you would still be working on projects driven by someone else. 

Having one or more individual papers would be one method of doing that. Being lead author on a paper in a field where order denotes role would be another. But for a PhD student applying for postdoc positions, their references will still play a big part in whether they are hired. Their supervisor should be able to include in the reference what part the student contributed to the paper.