Why include frequency dividers in this PLL circuit?
There are many subtleties to PLL design, in addition to whether things will work fast enough.

Obviously, the phase detector (PSD) has to work fast enough. The 3-state PSD in analog's answer requires a time delay in the feedback path. Its linearity improves as the delay increases, so there is a speed tradeoff.

The rest of my answer is going to concentrate on the often overlooked effects of PSD saturation.

A typical phase detector will saturate at a small phase offset. The 3-state saturates at +/- 1 cycle, though other types will often not go that far, and some can be built to go further. This saturation has some interesting consequences.

Let's say the PLL is designed to recover the carrier from an FM modulated signal. If the phase deviation of the signal exceeds the PSD saturation range, then the loop will go non-linear, which could cause problems depending on what the recovered average frequency signal was going to be used for. Putting a /16 divider in front of the PSD effectively moves its saturation level to +/- 16 cycles, so it can tolerate a much larger phase deviation before going non-linear.

Let's say the PLL is designed to rapidly acquire lock when presented with a new signal. Let's assume the PLL requires some particular bandwidth, for noise performance when locked, which means a particular gain round the loop. When far from lock, PSD saturation will limit how fast the loop can be driven towards lock. If, without changing the total gain round the loop, we divide the frequencies by 16 and multiply the analog gain after the PSD by 16, then the total loop gain and so loop dynamics when in lock remains unaltered (can remain essentially unaltered, see comment discussion below). However, the saturated PSD will now drive towards the lock point 16 times faster when out of lock.

As divided PSD like this will result in an increased contribution of PSD noise in the locked bandwidth. This may or may not be relevant in any particular situation. Different PLL applications will have different specifications, and so different tolerance of PSD noise. There is no one-size-fits-all answer.