I enjoy the dialogue with others and the opportunity to learn about this cool new car! I’m not a mechanic (but I play one on TV... J/K), so can’t accurately comment on extent of potential damage. But if Honda is flagging the risk in all their manuals, I think it’s worth trying to avoid as much as possible.
I know Honda made “brake override” standard on all cars starting 2011/2012, calling it “Brake Priority Logic.” The logic allows the brake pedal to override the accelerator if both are pressed at the same time, and addresses the safety risk of a stuck accelerator pedal. It seems like this logic disengages the transmission if both pedals are pressed accidentally or ‘occasionally’ as you mentioned. I think the risk for damage depends on how quickly the logic kicks in; any lag in the logic could mean cumulative damage over time.
I also just noticed that the INSIGHT, ACC HYBRID, and CLARITY owners manuals mention risk for “driveline damage” rather than “transmission damage” mentioned in the ACCORD and CIVIC manuals. I think the wording difference is intentional and based on operational and programming/design differences in the model groups. The driveline (i.e. everything after the transmission, like axles, wheels, joints) is technically separate from the engine and transmission.
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P.S. - the notice for the 2016 Civic Sedan online manual is on p467, and for the 2014 Civic Sedan online manual on p341. Also for completeness, the model years I cross-checked for each online car manual were the 2018 Clarity PHEV, 2018 Accord Hybrid, 2018 Accord, and 2018 Civic Sedan.