But this is precisely my question: in what way does splitting the code into many small files help with that? Personally I find jumping between many files (especially when they are located in various directories on various levels in the fs) pretty annoying...

Of course, that probably depends on the nature of the project. Having all backend code of a web app in one file and all the frontend code in another would be very inconvenient. OTOH, I have no problems with having e.g. multiple React components in one file...