The head has to spend a much higher portion of it's time being positioned from one read location to another when you ask a spinning media drive to copy from more than a single location.
Normally, when a drive isn't overly fragmented, the head seeks to the beginning of the transfer and then doesn't end up moving a whole lot. This isn't the case when you copy two or more things at once. The head seeks to the first location, starts copying, then at some point, usually determined by the copy algorithm, seeks to the second copy location, begins copying there for an amount of time, then moves on to any further copy points, or back to the original location.
This seeking is a big waste of time. You can visibly see it in transfer rates when copying from multiple locations. The sum of the multiple transfers will never equal the total of a single transfer. I would put the overhead in the neighborhood of 20% speed reduction, using back of the napkin math. It will always vary per individual hardware device, but in no case will multiple, simultaneous transfers ever be better than queuing or sequentially started transfers.
As far as damage to the mechanical drive, it's unlikely you could even measure the impact on useful lifespan for most consumers. I would only concern for drives that are mission critical, are near end of life, or routinely see heavy usage. Drives that are subject to high duty cycles should already have some sort of mitigation in place to reduce workload as much as possible.