... anyone who didn't socialise for reasons of age or infirmity would not be attainable.

Then there are people who are away from home, perhaps staying in London or Bath much of the time.

The route to some neighbours might have parts that were unwalkable eg having to cross streams, so only a carriage or horseback will do. That would make them not attainable perhaps.

Then there's the social class - there might be some farmers within walking distance who aren't wealthy enough or own enough land to be classed as gentry - I wonder if JA means that these would also come into the not attainable.

I doubt that the class thing goes the other way.... eg there is unlikely to be a Peer within walking distance as Sir John is the major landowner and if JA meant there to be a Peer so close, then I think she'd have mentioned it.