It is one of the biggest (mostly) myths regarding bandsaws, but it has sold a lot of quick releases...
The only real benefit is it prevents poor quality tires from taking a set and thumping for a while until the spring back out.
There was a youtube video that pontificated that you need to release tension or else the day/night temperature shifts would work harden the blade. I ask if he lived on Mercury, because if this happened on Earth all or steel bridges and buildings would be falling down around us. Undeterred he maintained he had "seen it".
I release tension only when I change a blade, I know one of my saws has the blade constantly under a tension of ~30k psi for over 9 years with no ill effects that I can see.
Of all the laws Brandolini's may be the most universally true.
Deep thought for the day:
Your bandsaw weighs more when you leave the spring compressed instead of relieving the tension.