Corrosion will destroy the tank's fittings/liner. Quickly.
So quickly, in fact, that it is mentioned multiple times in the installation manual to not do lots of things (no salt-fed softeners in bold/red/all-the-things).
While this may be true (have no knowledge | how does it work w/o salts?), the OEM will immediately void your warranty if you use any sort of homeowner water softener, per both Rheem and AOS installation manuals.
I have both; mine are warranted "platinum|10yrs" — why chance it?
water softeners in general are pretty bad. they're not great for your health, they're terrible for your soil. and the benefits to pipes and appliances are marginal at best. i completely shut down my water softener.
> the benefits to pipes and appliances are marginal at best
It probably depends on how hard your tap water is. My tap water is really hard. because it all comes from a river fed via glacial runoff in the mountains, so a water softener makes a huge difference, to the point where the water even feels different in the shower. But if your water source is naturally softer, then I can see that it would make less of a difference.
I'm curious why not? I can't immediately think of a reason why that would be bad, but I admittedly know hardly anything about plumbing.