The problem with this attitude is that you're missing out on reading material that reflects in incisive ways on genuinely contemporary issues in ways that Dostoevsky can't. Obviously books from the past can and do enlighten us about the present, and they don't literally have to talk about CNN to be clarifying about the nature of propaganda, but there are limits to what Plato can tell you about a world with 8 billion people in it.
In a way, your attitude is akin to only reading scientific articles from more than 50 years ago because those have "stood the test of time." In science, you can see how silly this is - not only is that material often just wrong, undeveloped, etc, but relegating yourself to only papers older than 50 years would leave you totally blind to contemporary scientific progress, including whatever seeds are presently germinating that will change the world in the future.
In a way, your attitude is akin to only reading scientific articles from more than 50 years ago because those have "stood the test of time." In science, you can see how silly this is - not only is that material often just wrong, undeveloped, etc, but relegating yourself to only papers older than 50 years would leave you totally blind to contemporary scientific progress, including whatever seeds are presently germinating that will change the world in the future.