With the highly-subsidised nature of printer (it's the razor model: provide the razors cheaply, make up on the blades), the burner route is actually reasonably affordable. Particularly if your one-time use is a high-volume printing.

The burner model provides little security in North America. Big box retailers record device serial number to prevent return fraud. It is known that retailers sell transaction information. It is also known that retailers use facial recognition, wifi, app location data, and bluetooth beacons to identify customers, even customers who pay in cash.

It stands to reason that retailers link transaction information--including serial number--to unique individual identifiers. It is possible this data is traded.

It is depressing that people in Western democracies have to worry about authorship identification via printers the same way people in the DDR had to worry about authorship identification via typewriter. But here we are.

There are numerous commodity markets in which indirect purchases are commonplace.

These might be informal (e.g., used appliances) or organised (straw purchasers or organised purchasing of burner phones, the latter was a subplot of The Wire.

Of course, utilising previously used devices might itself lead to traces for those printers, though that's probably a relatively low risk: the likelihood of any given printer producing output that's generally identifiable is relatively low.

That said, a fair point and consideration for anyone facing this threat model.

You could do the less shady version of this, which is to just buy a second hand printer.

How does new or used make it more or less "shady?"

Buying things second hand is something normal people do. ‘Pay someone else to buy a printer out-of-state in a store with cash,’ is not.

Both avoid store registration though.