I blame insurance companies. I can't speak for those south of the border, but up here the cost to insure (when you find a company that will insure a supersport) is painfully expensive. I honestly think that if they could retain the same aesthetic appeal of the 06-12 Daytona with a 3 cylinder sub 400cc engine (think of a cbr 125 x 3) they would have a massive target audience. No one, no where, at any time has ever said that the Daytona is anything less that one sexy b!7ch, but I know of a few people that won't buy one because of the added costs of owning one.....namely insurance. The problem they would face would be to keep costs low, which again I think could be manageable. With that size range for a bike, the company couldn't sell it for $12000, no one would buy it, so they would have to cheap out on parts on the bike (forks, shocks, MC, brakes, wheels, etc.). This, I find would also be acceptable, if they cheaped out in a way where upgrades could be had without extensive modifications. For example, use unadjustable USD forks, but keep the same dimensions of the forks that were used on previous/current Triumph motorcycles that are adjustable. So that if you want adjustable forks on your 375cc Daytona, buy some new/used ones off a 675 Daytona, change the springs to account for the weight difference and ride on (much the same the ST3 guys do). You want an adjustable shock, get one from a 675R, etc.
As far as competition, the Daytona easily trumps all the 300-500cc bikes on the market in regards to aesthetics, so if it were easily upgradable and priced reasonably, I can't see why it wouldn't dominate the segment. And when taken into consideration the fact that this is the largest motorcycle segment with respect to global sales would potentially make for a very profitable venture.
As much as I love my 675, if my insurance would drop from $150/month to $60/month (almost 38 years old with clean record....DAMN YOU ONTARIO!!!), I would be all over a 375. Unlike some/most riders, I know I'm not a great rider and I can't proficiently use the first 60hp that the bike puts out, let alone the next 65hp. So in essence, I'm paying a lot for insurance each month because I love the look of the bike, and I love the smooth 3 cylinder engine. Make it smaller, save me money, and I'm in.