wut
You pretty much answered your own question, but anyways. It is worth noting that limited supply does not apply to PoW coins only, and that there are PoW coins that do not limit their supply.
That being said: One effect of the halvings that often gets ignored, yet in my opinion is worth a mention, is that it ultimately keeps Bitcoin's power usage in check. Assuming Bitcoin's price finds a stable level, each halving will see miners drop off the network and power usage reduced as a new profitability equilibrium is found.
Another thing I find interesting about Bitcoin's halving is the 4 year cycle of sudden decreases instead of a more gradual schedule. My pet theory is that this 4 year cycle coincides with the public's attention span, causing upward price pressure and therefore media interest whenever the general public was just to forget about Bitcoin.