Fibers themselves have an extremely high bandwidth in principle. Pretty much all the wavelengths where they are transparent enough to transmit light such that you can still detect it at the other end.
Where the fiber itself is the limiting factor is dispersion, ie. since all signals have a bandwidth themselves, their 'red' and 'blue' portions travel at different speeds. So if the fiber is long enough and your signal modulation is very fast, at the detector end the square input pulse will be rounded enough that you have trouble distinguishing it from the previous or following one.
The strongest limits on the usable bandwidth come from the lasers and detectors that are being used. To get all the different channels in and out while keeping them separate, you need lots of narrow band filters and modulators/demodulators. That part of the technology is expensive, but is more often replaced/upgraded than the fiber itself.
The above is mostly relevant for long-haul fibers.
FTTH uses only a very small portion of the bandwidth that long-haul fibres use (Think e.g. of bundling in parallel all the FFTH fibers in Australia being a much, much thicker cable that what is laid into the ocean or between territories). You will almost never use the actual optical bandwidth of FFTH fibers, since you couldn't afford the electronics and laser to modulate and demodulate.
Finally, a human being (optical resolution of the eye being 1 arc second) can probably not process much more information than about 4 HD channels would pack (sound is trivial in information density compared to video, so is touch, smell), so there appears to be not much need for an individual to be connected at download speeds that substantially exceed the limit of about 4 HD channels incoming and 4 HD channels outgoing. Multiply this by the size of a family.
FFTH optical bandwidth likely already exceeds our biological capacity to process, only the price of the electronic side might remain a practical limit for a few years.