IIR filters are very sensitive to quantisation errors.
The higher the order of the filter, the more it suffers from quantisation effects: because the filter is more complex, and so the errors accumulate more.
In fact, IIR filters are so sensitive to quantisation errors that it is generally unrealistic to expect anything higher than a second order filter to work.
This is why IIR filters are usually realised as second order sections. Most analogue filters (except for Bessel filters) are also usually realised as second order sections, which is a convenient excuse but not the real one.
Second order sections can be combined to create higher order filters: