No, 60s cars were rigid boxes that did not crumple --which because of a lack of other safety features meant you got ejected or got banged around inside this metal box. These things allow you to get squished inside the foil box.

So the whole rigid box thing is kinda a "they dont make em like this anymore" myth. Here's a 1959 Chevy crashed into a 2009 Chevy https://www.youtube.com/watch?v=C_r5UJrxcck. They both crumple, but the 2009 only crumples in the crumple zones. The crumpling on the 1959 impala is more spread out and you can see includes more of the interior

It's less about that sort of crash and more about small fender benders. You're likely to get much more bumper damage hitting a car at 5 mph in stop and go traffic in a modern car. (The upside being, of course, you're a lot less likely to snap a pedestrian's leg in a similar hit.)

More bumper damage sure, but even at a couple miles per hour, a car where the bumper bolts straight to the frame moving at a couple miles an hour has to dissipate that energy. I'd expect to see some bent metal. My 82 bronco actually has a foot of steel bars that act as sacrificial bumper mounts so the frame doesn't take that impact.

A 60s Buick would not lose against a pinata.

The cars in the 60s were rigid. This meant that, by and large, the car did damage to everything else until that threshold was passed.

The problem was two fold:

1) You tended to get thrown around inside the rigid box since internal restraints weren't very good (poor seatbelts, poor headrests, no airbags, etc.).

2) Once you finally had enough energy to get past the failure point, the car collapse was uncontrolled. This generally meant that the steering column got pushed into the driver.