To extend the analogy: what do you do if grandma comes and fills your house with stuff? You need space to work, so you go and drop it off at the self storage place, but what if she just keeps filling your house up?
The OOM killer will do absolutely nothing until both your house and the whole self storage place are totally full. By that point, you've spent a huge amount of time just driving to and from self storage, so you haven't had time to do any actual work; it would probably have been better to tell grandma that you don't want any more stuff once she filled up your house for the first time.