Earlier quoted context omitted.
Yes, you are missing the other attack. Someone can take advantage of already existing lines of credit, credits cards, etc. which they presumably will not be able to do if you pay for everything in cash.
Obviously, but I guess I don't see how that relates to the article at all.
It relates to the article in the following obvious way. A freeze on running a credit report means that someone cannot run your credit report. Without the ability to run your credit report, someone cannot discover your existing accounts, limits, addresses, and balances by running your credit report.
You also wrote: Equifax et al don't particularly care if you pay cash, they have some form of record on you either way.
This is not correct. Equifax and the other bureaus do not have a record of you on a credit report if you always pay cash and never apply for or run a credit report.