Only if you want to minimize the total complexity, which is almost never a good idea. What is more important, is the minimum amount of complexity needed to be understood in order to make a change. If you are able to test a small subset of components in isolation, you can also understand them in isolation, and modify them without the need to understand the whole system. I'd rather read 20% of 110% code than 100% of 100%.

The advice to write mostly integration tests is a terrible one. Particularly when they test integrating of everything. When such tests catch bugs, they don't tell where the problem happened. They also take long time to execute.