What happens to a MacBook's battery once it reaches the maximum cycle count?
As it says on the page you've linked to (emphasis mine):

Batteries have a limited amount of charge cycles before they're considered to be consumed. Once consumed, a replacement battery is recommended. You can use your battery after it reaches its maximum cycle count, but you might notice a reduction in your battery life.
Knowing how many charge cycles your battery has and how many are left can help you determine when a battery replacement is required. For best performance, replace your battery when you reach its maximum cycle count.