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The natural tendency of the input side of the transmission is also to increase rotational speed, which is logical because it's changing ratios to allow the engine to rotate faster
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The natural tendency of the input side of the transmission is to continue with the same speed. Sir Isaac Newton was the first one to discover that. There is no natural tendency of things to spin faster on their own :-).
During a gear change some parts of the planetary have to accelerate, some have to decelerate or even stop. Some have to adjust to input shaft speed, some to output shaft speed. The point is that if a part speed is not already equal to the required speed, a slippage in a clutch has to take place. Slippage = wear.
Nevertheless, given that 3rd gear is typically the first one to fail, I can see a point in that downshifts are less damaging - in 3-to-2 change high clutch will be disengaged quickly, it can be done very quickly - it will not cause any shocks, just let engine rev up freely, and in 4-3 and 2-1 changes it is not involved at all.