sorry to dig this up
I have to ...wait....
it is my duty as a human being to correct some misconception

if you take the effort to try this out
the logic will come to you as to how to wind the spring onto the wire
even with a strong wire you still can do it

the 2nd is that "soft" wire as you claim give no support, thus back to square one (breakage at the head)
...is wrong

unless you want the wire to hold up to strong tugging
any normal wire that have frayed area at the head is due to normal usage
the problem with normal usage, is the wire is to pliable while the head is to rigid, even with the included pliable bits
the spring is made of metal, which is ductile in nature, and the spring material is rigid regardless of size
it is by design that the spring can be bend 180 without crimping (so much empty spaces in between)

so the function here is that when you start to bend the wire
the spring held the area nearest to the head to avoid majority of the force applied to that area
the spring will distribute the force evenly though out the whole body of the spring

so in a way, a too strong of a spring is bad for this trick as well
as the area after the spring, the wire faces the most forces applied, as the strong spring is less likely to bend

so the best is to find the cheap spring in those clicker types of pens
remember the spring act as a exoskeleton to the wire, distributing the force through out the wire at the rigid head
and preventing the wire being bent at a specific place