The cage had many iterations, the density of the cage increased and so the distance of the cage from the propeller. The propeller got replaced with a plastic one with rounded edges (though probably to save cost not as much for safety), so even if the cage is removed and you touch the propeller it isn’t that dangerous.
I don’t know what country you are in, and it is possible that in some place there might be dangerous fans, but if you can buy the bladeless Dyson, then chances are that stores also sell only modern fans, unless you’re purposefully buying an antique somewhere.
My experience differs.
A lot of time came since we had fans like this: https://i.pinimg.com/originals/24/55/85/245585f84697075b625f5fff32089e07.jpg
The cage had many iterations, the density of the cage increased and so the distance of the cage from the propeller. The propeller got replaced with a plastic one with rounded edges (though probably to save cost not as much for safety), so even if the cage is removed and you touch the propeller it isn’t that dangerous.
I don’t know what country you are in, and it is possible that in some place there might be dangerous fans, but if you can buy the bladeless Dyson, then chances are that stores also sell only modern fans, unless you’re purposefully buying an antique somewhere.
Here is an example https://www.amazon.com/s?k=desk+fans