Too many indexes can cause significant performance problems if RAM is short. If the indexes are actually used (rather than sitting idle on disk because other indexes are better choices for all your applications' typical queries) then they will “compete” for memory potentially causing a cache thrashing situation.

But yes, the issue with too many indexes is more often that they harm write performance.

A related issue is indexes that are too wide, either covering many columns or “including” them. As well as eating disk space they also eat extra memory (and potentially cause extra IO load) when used (less rows per page, so more pages loaded into RAM for the same query).

Both problems together, too many indexes many of which are too wide, usually comes from blindly accepting recommendations from automated tools (particularly when they are right that there is a problem, and it is a problem that a given index may solve, but fixing the queries so existing indexes are useful could have a much greater effect than adding the indexes).

Mostly because of overlapping indexes. Then if there are include columns it may get out of hand. Not too difficult to achieve. Just blindly follow recommendations from a tool or a cloud service.