Linz, Really a pretty good question. I think there's a couple of answers. First is that there is a tie to the 'Old' Triumph and the T140 triple so it has become an 'associated' Triumph characteristic...similar to Ducati's desmo valve train.
In motorcycles the first triples I remember are the Kawasaki two strokes. Suzuki came out with a water cooled two stroke triple and Yamaha had an air cooled 750. The design pretty much died out in the '80s, AFIK...the HP wars were on.
The four cylinder bikes could make more HP because of their lighter reciprical weight (valves, connecting rods) allowed higher RPMs. Torque suffered somewhat, however.
The twins make more torque because they simply have a bigger bang. They can't rev like a four cylinder because their thrashing parts are just too heavy. (Yeah, race versions of twins like the RC51 spool very high, but they're made of pure unobtanium.)
The triple is a mixture of both, a compromise.
FWIW, there are fours being tested as twins...two cylinders firing at the same time in a 'Big Bang' config. Still not quite as bike friendly narrow as a triple.