How is it squeezing out other traffic? A packet is a packet, under the net neutrality model all packets are routed equally. Capping packet flow from a provider would be like Subaru owning chunks of the national highway and setting a limit on the number of Toyotas that are allowed to be driving at a time. If Verizon doesn't have the capacity to support the evening demand, they should increase their shitty infrastructure so they can deliver the service that they sold to their customers.
And what if I want to compete with netflix myself? They have the cash to make a deal with Verizon, I don't.
Most networks see a degradation in performance at peak times. That reduction in performance can result in all types of behavior. You may not watch a clip, may click away from a site etc that's loading too slowly (and that would otherwise load fine and capture your view a few hours earlier)
And what if I want to compete with netflix myself? They have the cash to make a deal with Verizon, I don't.