I think the photo says it all.
I mean, sure, I probably own more than three d4s, but do I know where they are? No. And do I care? No.
Even in the contexts in which they are relevant (like, Level 1 Magic Missile damage or whatever) you do tend to look at a d4 and wonder if it's even worth it.
I've talked about a lot of qualities I value in a dice over the last few weeks of #diceday - I've talked about ease of reading, variable distributions, rollability, hand-feel, aesthetics... I never talked about how painful or otherwise it is to tread on one accidentally discarded on the floor because, for every other dice that issue simply doesn't apply. But these little b*****ds are pure, polyhedral evil.
OK, before I hit peak hyperbole I need to acknowledge a few things about d4s that aren't an unmitigated disaster:
They are very difficult to cock.
They look cool.
They are kinda interesting in a exploding dice scenario.
Let's take those one by one. Number 1 is obvious and easy. d4s are the most bottom-heavy of all the polyhedral dice, so even if they don't land completely flat it ought to be obvious what their result is - assuming they were easy to read, which they categorically aren't. Even dice manufacturers can't decide on the best way to put the numbers of a d4 to make it legible. The photo above has two different approaches (numbers at the base versus numbers at the apex) and those are far from the only approach designers have taken.
Number 2 is undeniable. The d4 is the weirdest-looking of the polyhedrals. It really looks like a magic crystal. It has echoes of the pyramids (already associated with mysticism and other fruit-loopery) but requires a momentary consideration before one spots that they aren't conventional pyramids. And the fact that we can't decide how to mark them for easy reading just underlines how weird/cool they are.
Number 3 applies in games that use multiple polyhedral dice and an "exploding" mechanic in which you re-roll dice that show the maximum value and add the new score to the old score. So an exploding d6 that rolls a 6 can be rolled again for a total result from 7 to 11 but, if you roll another 6, you roll it AGAIN for a total result from 13 to 17, etc. An exploding d4 is interesting because you have a 25% chance of getting an exploding result, and then a 50% chance of rolling a total result over 6, for a total 12.5% chance of rolling a result higher than a 6. Am exploding d6, of course, has a 16.67% chance of rolling a total result higher than a 6. Whether this is significant will depend a lot on how the game in question works, precisely, so it's a pretty niche advantage if it even is an advantage.
Frankly, the only reason I mentioned it was because, otherwise, the d4 is a mostly-pointless dice. Whilst, at the same time, of course, being the most pointy dice of them all. Now that's irony.