Even if you replace Verizon's router, presumably they have upstream nodes that they could monitor your traffic with just as easily. You'd have to replace all of

Even if you replace Verizon's router, presumably they have upstream nodes that they could monitor your traffic with just as easily. You'd have to replace all of Verizon. The Verizon router is like any other intermediate node on the Internet: don't trust it. Removing it won't really affect your privacy.