In terms of fast time resolution, you have correctly identified a niche for photometers. Another point in their favour used to be that they were much more sensitive in the U-band than CCDs, but I think that newer CCDs can almost match or surpass the U-band response of photometers.
CCDs take quite a time to readout. The faster you read them out, generally speaking, the higher the readout noise will be. By comparison, the output from photometers can be very fast indeed with little impact on the noise characteristics. One of the beauties of photometers is also that they give you an instant readout of how many photons have been detected, requiring little analysis to provide real-time monitoring of signals.
However, things move on. So now there are CCD instruments that can work on extremely fast timescales. An excellent example of this is a UK-built and operated instrument called ULTRACAM, which allows data-taking at 100 Hz and which uses a special "drift" mode of readout to achieve this.
Back to your main question - what are the scientific objectives of such instruments? On the link I provided above you will see a series of press releases that describe some of the science. These range from measuring the transits of Trans-Neptunian-Objects in front of background stars; examining detailed time series of flares on magnetic stars; investigating the eclipses caused by white dwarfs passing in front of companion stars; looking at the flickering output from accreting black holes; attempting to get phase resolved light curves of the optical emission from rapidly rotating pulsars and much more.
A rule of thumb is, that if you are able to obtain a time resolution $\Delta t$, then you are probing size scales of $\leq c \Delta t$, where $c$ is the speed of light. Thus if you can get a resolution of 0.01s, this corresponds to size scales of $\leq 3000$ km.
As to whether a photometer would be good on an 8-inch telescope, I'm not sure. When I was a student I used a photoelectric photometer on a small telescope to (i) study the scintillation of stars as a probe of conditions in the upper atmosphere - e.g. Stecklum (1985) - which has timescales of order $0.01-1$ seconds. (ii) To monitor "flare" stars with a time resolution of about a second in an effort to get real-time information so that spectra could be obtained at various points during a flare.