The first sentence is true. I don't think the second sentence follows. They collect the fee and do basically nothing. The TLD registrars run the DNS for their domains, but they do it through the root servers:
https://www.iana.org/domains/root/servers It would be hard for ICANN to muck with the root servers, but I'm not sure about their business relationship. Probably something like a peering arrangement.
“The first sentence is true. I don’t think the second sentence follows. They collect the fee and do basically nothing.”
The fees require a database of all domain names.
And the Swedish plan assumes that individual domain names are affected.
Secondly, I can’t imagine Sessions and Grassley and Gohmert being overly concerned about a minor shift in domain names:
http://www.freerepublic.com/focus/news/3394704/posts
They plan on ICANN specifically being used to ‘oversee’ the internet. For example, a fine for ‘hate speech’. Collecting a fee? Well, that fee could be a million dollars a month or more.
Please note the testimony of Paul Rosenzweig — I wrote summaries of it and link to it directly.
Final point — ICANN has multiple branches. One such branch processes the IP address — the number code of each domain name.
The Address Supporting Organization (ASO) deals with policy making on IP addresses.