Cpus without ipgus are somewhat cheaper, and the pc will have a dedicated gpu from the very beginning. Is there a reason to pay extra for a cpu with a igpu in this case? Would the pc automatically switch to igpu to save power while not gaming/working? Anything else I am not aware about?
It depends. Are you going to compromise on performance to get a CPU with an iGPU when you plan to run a discrete GPU? If so then no, do not buy one. The chances of you actually needing the iGPU are low to 0.
If its a choice between the same performance CPU with or without iGPU, then for a few extra bucks its worth it for troubleshooting purposes.
If you're using a discrete GPU then the iGPU does absolutely nothing at all. There is no switching or anything, it just lies dormant. You can configure it to run a secondary display if you so choose. This can be problematic sometimes, but usually works.
In terms of current CPU shopping, all current AMD 7xxx series CPUs have an iGPU, Also most Intel Processors of the current generation have an iGPU, theres a few models you can seek out with it removed. If you roll back on AMD to the 5xxx series, most do not have an iGPU, and you are better off with the ones without it, performance wise.