> Unless you can eliminate fraud
Which is exactly the purpose of good security measures.
Bad or nonexistent measures and an insurance against fraud slapped on all prices is a local maximum. Good security measures which really push back the fraud and allow prices to drop the insurance premium is obviously a better local maximum.
You also don't have to eliminate 100% of fraud, just make it so rare that you can basically ignore the risk because it happening to you is as unlikely as being struck by lightning (or any other risk of life that people are comfortable to ignore due to it being vanishingly small). The classic credit card fraud with magstripes was the exact opposite of that: there was almost no credit card owner who didn't get hit by it, and while people generally didn't lose money due to reimbursement by the cc companies, they still lost time and nerves over some stupid interruption in their lives that was entirely unnecessary in the first place.
I myself had one of my cards suddenly deactivated by the bank because of alleged fraud (it wasn't even real fraud, just some heuristic going crazy over an actually intended payment). I was on a cruise ship in the Caribbean sea when it happened and all of a sudden couldn't pay my beers with my ship card anymore. Fortunately I had a second card with me that was working so I continued using that, but in order to switch my onboard expenses account over to it I had to spend some time at the customer service desk on the ship, where there was a row of passengers standing at phones, occasionally speaking with someone in various languages, but most of the time they seemed to be waiting in silence for some kind of response. It took me a few minutes of overheard conversation until I realized that these guys were in the same spot that I was, but less well prepared; they didn't have another credit card with them and thus had to call their banks back home in order to get them to unlock their accounts again.