The premise of the quedtion is wrong--they do make these cars. See the Scion FRS. Also Subaru has a car that looks just like it, but I cannot remember the name.
Also I would argue the Mazda Miata targets this style, and I have seen a Honda car that looks quite similar to the Miata as well.
I have seen a Honda car that looks quite similar to the Miata as well
That would be the S2000. It was a bit upmarket from the Miata and remained on the market longer (10 years) than anything else that tried to compete head to head with the Miata.
Gosh, I'd love another S2K. Hopefully once the Supra launches, Honda will be more motivated to do a more hardcore sports car, possibly with the Type R Civic drivetrain in a RWD roadster configuration.
Also I would argue the Mazda Miata targets this style, and I have seen a Honda car that looks quite similar to the Miata as well.