why can't a provider pay for a similar "bigger pipe" TO the ISP?
Well they could, but the provider doesn't have a pipe to the ISP, the provider has a pipe to their own ISP (Let's call it BackBone) and the consumer ISP also has a pipe to BackBone. The provider and the consumer ISP are both paying for their own pipe and the Customer is is paying the consumer ISP for access to that pipe. In this diagram there is no business relationship between e.g. NetFlix and Comcast and any effort by Comcast to get NetFlix to pay is basically extortion (nice user base you got there, be a pity if something happened to it). It might also be fraud as the Comcast customers are paying for a connection to the broader internet, not just those entities that Comcast "likes".
If NetFlix wants a faster pipe to Comcast customers they could certainly negotiate with Comcast to by a direct connection into the Comcast network and cut out BackBone.
None of this is meant to imply that Comcast can't do traffic shaping on their network, but that shaping should be part of improving the customer experience, not blackmailing content providers.