Technically, they did make a 250cc sport tourer, the ZZR-250.
What is a “sport tourer”? A bike that can tour comfortably for a long distance and be sporty in the twisties.
Frankly, there are two types of sport-tourers, big touring bikes with big sport bike engines (Concours, FJR, F800ST) and then are smaller sport bikes that are last gen, and have their head angles slackened and a more padded seat added (ZZR-600, Katana, VFR, although it was last a race bike 15 years ago and has just kept being developed as a road oriented bike).
A motorcycle is a motorcycle. People ride up to Alaska on cruisers, gold wings, CBRs, R6s, Ninja 250s and DR200s. People have circumnavigated the world on old 350cc Enfields and Nortons.
What can a VFR do that an SV650 with a windscreen and luggage cannot do? Or a Ninja 650 with locking givi bags (which btw, really is all it takes to turn that bike into a sport touring ride, lots of people really like the 650R as a sport tourer).
Take pretty much any motorcycle, change the seat to an aftermarket, and maybe put bar risers on it, and then add luggage, and you have a bike capable of taking you across the country.
Heck, a guy just posted on Advrider about his multiple trips across the US on a stock ‘busa, with his girl friend pillion the whole way!
The reason big bikes are used as sport touring bikes is simple: People want to load up everything they can, while still accelerating like the bike is unloaded and cruise smoothly well above the speed limit.
If you want one of the best sites dedicated to sport touring (and in fact, the people who designed the Sport Touring Advanced Rider’s Training course) look at CanyonChasers.net – Read their trip reports, and look at the bikes that come with them on their trips. Yup, lots of proper sport tourers, but also full on sport bikes, old standards, everything but cruisers in their ranks ( http://www.canyonchasers.net/travel/2008/md08.php ).
Read the roadwarriors section of advrider, or the quest section of ninja250.org – every bike imaginable has gone on a long, fun and rewarding trip.
Thinking bikes have to fit into some nothing more than specific niche is glossy marketing.
Ride what you bring.
The problem with the internet: Everyone gets the same font size.