Can I replace these many capacitors with just one?
The goal of each capacitor here is to smooth out the power supply of each WS2812B. When you power an array of LEDs, there is a good chance that a transient voltage drop will occur and create a flickering effect on your LED strip and most likely on other LEDs that are currently on. If you were directly powering a LED from the power supply, you wouldn't need a bypass cap. However, The WS2812B is a LED coupled with a integrated circuit. The IC is far more sensitive to voltage variation on the supply. The flickering will be caused by the IC going haywire. As it was pointed out on the comment, you would need a far bigger variation on a power supply to see actual flickering when directly powered.

By assigning one cap per circuit, you reduce the amount of calculation required to compensate. You don't need to take into account as much information. Also, you can place the cap really close to where it is actually needed. What is important here is the close proximity of the caps to minimize trace inductance. 

You can also take a look at this question for further details.