Is there any evidence that suggests that reading from a hard drive (instead of it just spinning idle) increases physical wear in any meaningful way? Likewise, is there any evidence of this for solid-state storage?

Yes. Hard drives have published "Annualized Workload Rate" ratings, which are in TB/year, and the manufacturers state there is no difference between reads and writes for the purpose of this rating.

(https://www.toshiba-storage.com/trends-technology/mttf-what-...)

For SSDs, writes matter a lot more. Reads may increase the temperature of the drive, so they'll have some effect, but I don't think I've seen a read endurance rating for an SSD.

Reading from it requires the read head to move, as opposed to spinning idle where the heads are parked on the side. Moving parts generally wear out over time.