Sorry about the late reply.
While blunt faces of stainless steel may not be obviously affected, fine, sharp edges like quality steel knife bevels are destroyed (the theory is) via abrasion, oxidation and or corrosion from the detergent that contains abrasives and harsh chemicals, and the heat and turbulence of the cycle. Under a microscope edge damage / changes can be seen and also subjectively tested
Sorry tba, I'm a knife nerd so worship all quality steel sharp things.
I said the same recently on VA (and also a bit of a knife nerd).
Polished stainless pots like All Clad become dull if cleaned in the dishwasher even though they are dishwasher safe and a knife edge or, in this case, grinder teeth edges will dull over time from the abrasives in the detergent. I'd be in no rush to do that, I'm happy to see the teeth are sharp enough to cut fingers because that means they are going to perform for their purpose rather than focus on mashing and tearing.
I've always likened the abrasives in detergent to a chaotic form of stropping where it's slowly polishing and rounding the edges.
It definitely won't "harm" 304 stainless but it can and will affect performance over time. That may not be something many ever notice enough to care about, but with my experiences and education with higher end Japanese knives I have become cursed with the knowledge that won't let me get past my own mind on it.
That and having bought the titanium version (looking forward to it!) I am going to spend time caring for it just like I do with all my nice things.
Editing to add:
Fun first post here for me after lurking for a long time!
I was actually thinking the super sharp teeth may be aiding in overall cleanliness when comparing a super sharp knife... cutting things like tomatoes, limes, etc leave little to no liquid on the cutting board because the edge is so sharp it doesn't tear the cell walls when slicing.
It's not the same mechanism for cutting here, but I wonder if that applies to some degree and allows cleaner grinds where the sticky stuff doesn't get broken free and released as much. This would improve the quality of the ground product too. Maybe I'm thinking too deep into it, I dunno.