There are only 5 main purposes for any vehicle: military, cargo, passenger, service, & sport.For me, the crucial piece of the jigsaw would be the "fighter"-type spacecraft's non-military applications. What use would the Federation have for such a class of small craft during peacetime/exploration? In the TNG ep "The Emissary", K'Ehleyr was shot into space inside a torpedo/probe to intercept the Enterprise-D. That shows me that the whole one-man-ship idea can be done, and at warp speeds to boot.
So the questions remain: what would such a one-man or two-man ship look like, what kind of nomenclature would Starfleet give it, and what would its applications be for both military and non-military (exploration, transportation, etc.) purposes?
A single-man vehicle has definite applications in regards to racing sports. I would imagine the Star Trek Universe's answer to Formula One Racing, would be to strap oneself to a warp core & nacelle and see how far one can go before exploding, and how quickly they can get there. We have already seen Starfleet train cadets in single-pilot craft (albeit at sublight speeds) in the case of Nova Squadron's advanced pilot training course at the Academy -- so that's military. For service, I think a one-man or two-man craft, capable of interplanetary or interstellar ranges, would have enormous benefits to local law enforcement as cheap, easy-to-maintain patrol cruisers. Passenger-wise, I think an affordable private low-capacity craft might do for the STU what the automobile did in the 20th century, granting people more autonomy and independence in their transportation needs. As far as cargo, we already have the "work bee" shuttle, that can be modified to do a number of tasks.
The key is finding a way to get those smaller craft to be able to keep up with and out run some of their bigger cousins. Speed is definitely the key. I just wonder if that speed is possible in such a small craft?