I think that close reading is a skill that has to be developed over the years. It’s why we push reading programs for children, especially over the summer, so that they can keep developing their skills. We do this so that by the time they get to high school they can start fully developing these close reading skills and be better prepared for college when they need to be able to quickly read and analyze text every day.
I think that it is 100% possible to read too much into a text. If you over analyze a text, you will end up missing what the author intended for you to take away. If you think too much into it, you could end up changing your perception of whatever you are reading and changing it to whatever lens you came into the text with.