This makes little sense.
When the blade is tight, it has a load in it. Just sitting there nothing will change. The blade is not going to stretch just sitting there, if it could, the blade would just fail in use very quickly. The blade has to have the tensile strength the handle the load when tension. Just sitting there won't change anything, the load isn't changing or going over the limit of the blade. No different than a torqued bolt, it has to be strong enough for the pre-load, it won't suddenly snap/stretch just sitting there. When cutting, the blade will warm, thus get bigger thus get less tight, when it cools back to ambient temp, it will be back to it's normal tension.
Now if the concern is your shop changing temperature when sitting there, maybe, but since blade and saw are all steel, they will largely expand and contract as one.
I've never heard of people doing this, it comes across as just plain dangerous as others have mentioned. If there was a real concern the bandsaws would have an auto-tensioner type device just like belt drives and such. It could always limit the tension in the blade. Plus interlocks like Svar mentions.
Far as shafts and bearings. They too have to handle the static load of the tension, once they are designed for that, just sitting there loaded won't change a thing. If it did change sitting there, the bearings and shafts would again fail right away.
The saw has to be able to handle the loads the blade sees in use, this is going to be higher than just sitting there.
Maybe there is a concern about deforming a tire in one spot, but again, that sounds unlikely. Maybe there is a concern about parts rusting together just sitting there for long periods of time.
Look around us, everything is under load. We don't unload the stuff around us. It all either handles the load indefinitely, or it fails right away. Cycle life can come into play and that is what wears out a machine, but obviously that is when it's running, not just sitting there.
This might be a way to use fear to cause folks to regularly check their blade tension.