Not necessarily. You can have a softer spring arched correctly with reinforcing leafs and not sag. Geometry plays into it.
Or you can use different grades of steel. What really matters is the heat treat and steel types. It all comes down to the modulus of elasticity of each type of steel. Some can have a high modulus and bend and move a lot and return to its original shape while others could be stiff to start but have a very low modulus and won't spring back to its shape.
The heat treat comes into effect the modulus of elasticity a lot.
It's not a 1-1 comparison that stiffer lasts longer.
Look at the front coils for example. The 3.0 use a softer spring than stock, no sagging there. Icon uses stiffer.
When I took my hds off after 8k miles the leafs were flat. To the point when I carried them to the curb the weight or the leafs alone dropped the lower leafs so here was a gap at the top. They we're loose in the pack. The arch didn't hold at all
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