They're cheap and take up very little space
I am not a person who owns trivets. Or, at least, I wasn't until recently. I live in New York City and have a kitchen that is the size of many of the pantries my friends casually store enormous amounts of dry goods in. Trivets always seemed weird and fussy to me. Just use a kitchen towel! Who cares, live your life! But then again, I vacillate wildly between being a person who believes that all you need in a kitchen is a cast iron skillet and some willpower and a person who appreciates a highly specific gadget. What can I say, I contain multitudes.
I was finally convinced on the trivet front at Thanksgiving several years ago, when my then-boyfriend's mom brought out a container of what looked like Jacks and started sprinkling them over the holiday table. These were her Tovolo tumble trivets, and they were genius. They're made of silicone and keep hot dishes from scorching the table, but they also take up basically three inches of precious drawer space. You don't need to worry that they won't fit the dish you're using, as you can arrange them however you wish. The only downside is that it's possible to lose one, given how small and bouncy they are, but that hasn't been a problem for me.
Best of all, they are madly adffordable, at $5.99 for six or $11.99 for 32. They also make for a great, really thoughtful hostess gift at a dinner party or celebration. They're colorful, they're easy, and they're useful. Who can be mad at that?