This has already been covered many times but the design of the AT protocol requires a lot more resources than AP. Meaning it will be reserved for large organizations, while AP has a lower entry of threshold. I want both to thrive, but I prefer AP for small communities.
The AppServer, if you want index the full bluesky network (39M users) will run you about 200-300 dollars a month. Again, not really needed but you can if you want. There's also experiments people are trying out to only index smaller parts of the network, e.g. only users you follow which would mean hosting an AppServer would be even cheaper. FWIW, I like both protocols and want them to succeed, anything that gets people off of closed social media.