What incentives do researchers have for applying for NSF grants?
From a purely monetary standpoint, Principal Investigators benefit from grants in multiple ways: grants can be used to pay the PI's summer paychecks (faculty contracts usually mention that the salary is for 9 or rarely 10 months), grants can be used to travel to conferences, grants can be used to pay for hardware, including laptops, and so on. 

Without grants, a faculty would have to pay for those things out of their own pocket (which, in the case of the summer paychecks, just means "do not get paid").

About the part of your question about the NSF "pitching in", here is a quote from the NSF Proposal &amp; Award Policies &amp; Procedures Guide (Part I, Chapter 1, E) :"Unaffiliated individuals in the US and US citizens rarely receive direct funding support from NSF".