Surely though, the HOA and all that would likely be baked into a renter's price.

And you didn't need to go live in a HOA. I don't, and it's much cheaper.

Surely though, the HOA and all that would likely be baked into a renter's price.

Sure, the same way that the benefits of a fixed mortgage payment are baked into sale prices. The efficient market hypothesis would say that neither renting nor buying should be obviously superior in the long term, because if either was then people would bid up rents/prices until it wasn't.

And you didn't need to go live in a HOA

I pretty much did, unless I wanted to significantly compromise on other factors.