Would it be unreasonable as part of the service provided by airfields in return for the landing fee to expect a free wifi connection?
Quite reasonable, since they all have a phone line and you can get ADSL on the back of that for next to nothing these days. And the person collecting the money will probably be on pprune anyway
One needs to do more. One needs to provide a public PC. The cost of that is absolute peanuts these days.
In the wider context, travelling abroad, all this is wishful thinking and having mobile internet is absolutely the only way to go.
There are bound to be strips out there without a GSM service, and without a phone line, and their residents just need to make other arrangements. But this will be rare. I live and work in the countryside so I see poor signal levels all the time, but one can usually get connectivity, even if most of the countryside will not have 3G. You don't need 3G for any aviation preflight purposes.