Technically, I think it's not that instrumental goals tend to converge, but rather that there are instrumental goals which are common to many terminal goals, which are the so-called "convergent instrumental goals".
Some of these goals are ones which we really would rather a misaligned super-intelligent agent not to have. For example:
- self-improvement;
- acquisition of resources;
- acquisition of power;
- avoiding being switched off;
- avoiding having one's terminal goals changed.
Robert Miles' videos are among the best presented arguments about specific points in this list, primary on the alignment side rather than the capabilities side, that I have seen for casual introduction.
Eg. this one on instrumental convergence: https://youtube.com/watch?v=ZeecOKBus3Q
Eg. this introduction to the topic: https://youtube.com/watch?v=pYXy-A4siMw
He also has the community-led AI Safety FAQ, https://aisafety.info, which gives brief answers to common questions.
If you have specific questions I might be able to point to a more specific argument at a higher level of depth.