A smaller field of view would not necessarily help. The data transmitted back to Earth by Kepler was already limited by telemetry constraints and the portions of the CCD that were read out were already focused on small windows around (many) selected stars. Having a field of view that is at least 10 arcsecond across would be sufficient. What is more important is to make sure your star images are well-sampled. This is a bit of a problem for Kepler. The CCD pixels are quite big (4 arcseconds) to give a big field of view, but this is similar to the angular resolution of the telescope. This means all the light can fall in basically one pixel, which is not ideal for precise photometry. If you were focusing on one star you would make the field of view smaller but have lots of CCD pixels across your star image. This improves the precision of the photometry considerably.
If you were to construct a similar telescope designed to look at one star at a time, then in principle you could have a much higher telemetry rate for that star. Hence, if you had enough photons and a low CCD readout noise, you could take much shorter exposures and see finer detail in the light curve transits - maybe moons, rings, starspots etc. The standard Kepler cadence was 30 minutes for most stars and one minute for some of the brightest stars - see this link. A more rapid cadence would allow a much better characterisation of the host star through asteroseismology (e.g. mass and radius), which in turn leads to better characterisation of its planets.
To take advantage of the higher telemetry rates, it would be advantageous to have a larger aperture telescope, simply to collect enough photons. The angular resolution of the telescope is not that important if investigating obviously single , bright sources. You would need an absolutely enormous telescope (100m+) to resolve the disks or planetary systems of even nearby stars, so this is not really feasible.
A larger telescope would also allow you to split the light by wavelength and investigate transits in a wavelength dependent way. This is really important for investigating atmospheric composition and chemistry. This is perhaps the only area where focusing on a single star might be useful - because you could design a slit spectrograph to monitor the transit spectrum. On the other hand, these days it is possible to design multi-object spectrographs using fibres or slit masks, so overall I can't see any real advantage to having a telescope that is capable of gathering data for only one star at a time.
