There are at least several decks that almost qualify:
So, why is WBR rare?
Playing WBR means forgoing green and blue. What are you (typically) giving up when you do that? Mana ramp and color-fixing (G), countermagic (U), card filtering (U), card draw (both), and usually the biggest mid-sized creatures in the format (G) — basically a lot of the tools that help you cast big things faster or dig in for the long game. This implies that most WBR tournament decks will be on the aggressive side.
Top-tier aggro decks are all about consistency. Mono-red is the most enduring aggro archetype not because red somehow has all of the best and fastest aggro cards, but because this is a deck that just wants to curve out super-consistently in every game. When your whole strategy is to prey on decks that make themselves too slow or greedy or fragile in pursuit of raw power, you can't afford to slip on mana yourself. So multicolor aggro decks mainly appear when a format supports very consistent multicolor mana bases, above and beyond the level that enable successful multicolor control and combo decks, or in aggro-heavy environments where you're looking for some kind of special advantage in the mirror.
In some environments, such multicolor aggro decks are viable. However, WBR is a "wedge" color combo. Most seasons of Standard, Extended, and Block Constructed featured better support for "shards" (allied-color groupings, like WUB). Why play WBR when you can play Jund (black, green, red — black and green together give you removal as flexible as white's) with better mana?
In environments with even better mana, decks are more likely to just end up in all colors. Look at Koike's Zoo list above, or Jakub Slemr's five-color black weenie list from the 1997 World Championship. When it's so easy to splash for a powerful card like Tarmogoyf or Man-o'-War (1997 was a very different time), why not?
Martell's PT-Gatecrash list or Saito's 2006 list benefit greatly from mana bases that support all color combinations equally (since both Ravnica shocklands and the Innisrad/M13 "buddy land" megacycle equally cover ally and enemy color pairings). But they could just as easily have been very consistent two-color decks. After all, all three colors generally have a lot of overlap when it comes to aggro cards (cheap aggressive beaters and efficient removal of various kinds). So, why build three colors, especially WBR? I believe powerful multicolor cards like the eponymous Aristocrats or Lightning Helix and Hit are the main reason these decks ended up as three-color WBR. (How good is Hit? Apparently good enough to justify losing 8 life to a Dark Confidant flip when your deck can't even cast Run!)