Bad shocks will not cause vibrations or springs to sag.
Age & weight is what kills springs.
I have never seen rearching work or last very long.
Not true. The axle+wheels makes for a mass. The spring is, well, a spring. Mass-spring pairs have a natural frequency dictated by the square root of the quotient of the spring constant over mass. Without going into the physics, it is the same as a pendulum's natural frequency. That is the purpose of a shock absorber, to PREVENT oscillation. Some vehicles can get by without shock absorbers as the natural frequency is outside of the range of excitation.
The initial failure mode of a shock absorber is low frequency, this is the mass of the vehicle coupled to the spring. The final failure is higher frequency, the mass of the axle+wheels (unsprung mass) and the spring system. Note, there can be multiple modes of vibration, single wheel, coupled wheels and rotation about the drive shaft.
Now, what causes spring sag? Simple, cycles. Most of the big bump cycles do nothing. It is the higher frequency, lower amplitude cycles which do far more fatigue to the state of the steel. This is where the common (misconception) of spring age due to sag comes from.
Simple rearching without reconditioning is nearly pointless because the friction between the leaves is not addressed. The term here is hysteresis and it is from excessive friction. Full reconditioning with subsequent shot peening after re-arching makes for a permanent process. Shot peening restores the compressive stress in the outer skin of the spring, the most highly stressed portion of the steel.
There, now I am off my Mechanical Engineering soap box. No myth, just facts. The company I selected to re-arch my springs has been doing it since 1935 and still owned by the same family.