C'mon now, Soren. I know you know the answer to this, as we've all discussed this many a time around here over the years.
However, to recap this once again, I'm thinking there's probably TWO answers here.
First, there are many a Britbike owner who will associate all "Cruisers" with large lumbering Harley-Davidsons, which were always in a manner of speaking the complete antithesis of a lighter-weight and better handling British motorcycle. And this point does not even include the idea of a separate "sub-culture" of these different riders, which often includes their attire AND often even the manner they present themselves to the world.
And secondly, because specifically in Triumph's long history of manufacturing motorcycles, it wasn't until 2002 that Triumph even offered a "Cruiser", and thus to the many of Triumph "Traditionalists" out there, building a "Crusier" is "sacrilege" in their eyes, as once again, Triumph had no history in making this type of M/C until '02 and when it seemed as if they were "jumping of the Cruiser bandwagon" which was all the rage around that time and when H-D dealerships had waiting lists to purchase their bikes.
Now, regarding the R3 thing...my guess would be that the only reason any Triumph "Traditionalist" might appreciated those is that they can boast that their favorite brand makes the biggest and baddest mass-produced motorcycle on the planet, and EVEN THOUGH that might be the last motorcycle on the planet that they'd ever consider owning.