Shooting a DA Smith in rapid DA is not going to harm the gun, although being a precision mechanical device it will eventually need maintainence and parts replacement after thousands and thousands of cycles....I have been shooting / instructing and repairing / maintaining smith's for approaching 40 years ( duty guns and competition).
I will give you one example: M-65 4" bl K frame 357 mag (personal gun)...bought mid 70's.....shot 32,000 documented rounds thru this revolver.../ approx. 50% 357mag loads with 160 SWC's and the other 50% 158 gr RN 38 spl's......all DA....used to do rapid DA demo's with 6 rds under 2 seconds.
Plus I have dry fired the gun thousands and thousands of times.
Over the course of the 20 years that I fired this gun 32,000times, I had to replace three hammer noses, several hammer nose springs, two hands, two mainsprings, several locking lug springs.....had to retime the gun several times, and peen & dress the locking notches on the cylinder several times.
I know very few shooter's that put that many rounds thru one revolver, unless they are a competitor / serious shooter. But if they do, the Smith is up to it....it requires maintainence, occasional parts replacement and tuning like all precision machines....so don't be afraid of dry firing or live firing your Smith....they are pretty much immortal.