Galvanized Water Heater Straps be reused?
The claim that the previously applied straps cannot be re-used is mostly not true except for certain specific cases.

In general these can be re-used as you can see they are adjustable via those slots every half inch. These may have been cut to length on the original water heater but there is no reason that they can not conform to a new water heater that is slightly different shape.

But in a special case that the new water heater is a larger diameter it is possible that the slotted straps may now be too short to reach from their anchor points on the wall around the heater. As designed the straps have to come together far enough so that the bolt brackets can slip into the slots and the bolt is long enough to engage the two bracket holes. 

So it is possible that the original straps may be too short. Probably not uncommon as newer water heaters may very well be bigger diameter due to larger tank size or additional insulation  needed to increase efficiency.