> You have to take a topic you find interesting and read all possible related work in it
This is definitely the wrong way of going about a research project, and I have rarely seen anyone approach research projects this way. You should read two or at most three papers and build upon them. You only do a deep review of the research literature later in the project, once you have some results and you have started writing them down.
Unless you're already an expert in the topic a literature search is literally step 1 since you have to check if your idea has already been done before.
The usual justification is that if you don't do at least a breadth-first literature review, you can get burned by missing a paper that already does substantially what you do in your work. I've heard of extreme case where it happens a week before someone goes to defend their dissertation!