As a hobbyist welder I agree. Nearly all metals can be reworked without trouble. Some, such as Reynolds 853 get stronger at the weld joints.
Can you lose strength cutting off welded tubes and rewelding them at the same joint? Yes. But it may never be a factor.
I've built quite a few cages out of cro-moly tubing. Whenever we needed to rework a cage to make it fit the vehicle we always had two rules.
Never add to a piece of tubing.
Cutting tubes shorter was ok but the piece they were originally joined to was always replaced.
My buddy recently started welding ti. The equipent cost more then my mig setup + both my arc welders.