“Rivnut” sounds like a particular brand, and might well need special insertion tools..
The fasteners I had in mind – and have a small collection in reality – are different beasts.
They are Hank Bushes: nuts with a short, deeply countersunk shank. The shank is pushed through a close-fitting hole in the plate then riveted into a countersink in that. At work we closed them down with a simple dome-ended punch struck with a hammer. A more elegant version could be used in a fly-press or arbor-press.
The hexagonal ones’ sharp corners and slight undercut, give them a bit more grip in the material than a cylindrical one would. Their shape would also look right in visible places on a model, assuming suitable size.
This is a Hank Bush, or Hank Rivet Bush; the image from a fastener-supplier’s catalogue. Readily available but likely, now only with ISO-M threads.
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Another form of the many varieties of static-nut fasteners, has a cylindrical body on an elliptical plate with two small holes for rivets. Plus there all those spring-clip nuts and the like for thin sheet-metal work.
It’s probably worth inserting the screw with a spot of anti-seize grease on its thread, to reduce the risk of the bush rotaing when trying to remove the jammed screw.
(My steam-wagon chassis, built from 50 X 25 X 5mm HRS channel, has tapped holes wherever possible, and where the lack of a nut would not be noticeable.)