D4s are the unloved sibling of the polyhedral dice family. They have bad roll feel, and lack the drama that other dice rolls invoke. It should not be your go to dice roll. Where they shine is for the various bits of unplanned improvisation. In most rules-light OSR games like Into the Odd, and similar, when a character uses an improvised weapon it does 1d4 damage. If you are running your game using blorb principles, eventually you encounter a question from your players about something that is not in your prep. Time to make something up. Rather than just decide something by GM fiat, why not come up with a couple of possibilities and roll for it? Coming up with six possibilities on the spot is often too much, and by the time you roll you might forget what the first thing was. Four is an easy to manage number.

An example:

GM: You come across a book of poetry.

Player: What’s the poetry about?

GM: Good question. Lets see. Poems can be about love, heroic epics, melancholy, or silly. (Rolls a three on a d4) Looks like these are poems lamenting the transience of life.