The Piccadilly line isn’t owned by Heathrow but rather by TFL and so isn’t subject to inflated fares and is in the same zone as non-airport stations a comparable distance out from London.
Although all journeys between Heathrow and Zone 1 or passing through Zone 1 are charged the peak fare all the time, but that's a TfL thing.
You can get the local bus to Marsta, and pick up the regular SL trains there.
All within the Stockholm ticketing network.
That's what he said...
Sydney Trains has separate airport stations for international and domestic services, both privately built.
So you have to pay the access fee just to transfer terminals (though there is a less frequent free bus I think).
The access fee for transferring terminals is only $4.50 (so the total fare would be $7.30 or $8.50 depending on the time you entered). There are often 8 tph, but not evenly spread out.
The access fee is also lower if taking the train between the Airport stations and Mascot or Green Square.
The free bus is 4bph. There is also a paid bus which is $3.20 or $2.24 depending on boarding time, up to 4bph but not always reliable.
Melbourne Airport is served mainly by premium buses, for $22 single/$36 two-journey to the city centre. It is possible to use local public transport, but extremely inconvenient except to a minority of destinations. It seems that public transport is capped at $10 per day to anywhere in Victoria.
Brisbane Airport has a premium fare for its train service, about $35 return, but slightly cheaper online which gives you a PDF with barcode that gets scanned at the airport, but you must show manually to enter/exit at a barriered station. There is no local public transport at the airport but there is a free airport-operated bus to a nearby shopping centre which is served by a local bus. The only way to pay for the bus is by local smartcard, which has to be purchased at the airport. Therefore, you must pay the amount of the premium train fare even if you are not going to use the train. Fortunately, the card and deposit is fully refundable (you can buy with cash or card, but only refund to card).
Perth Airport was previously mainly served by local buses at the regular fare, but for a city which has become hostile to cash, the only way for a visitor to pay was by cash with no change. That was not too difficult when the fare was $5, but then they increased it to $5.10. Last year, a new airport train service commenced, though only to one of the two terminal complexes (there have been talks about closing the other complex at some point). It now appears to be possible to buy the local smartcard at the airport, I am not sure what other ticket options are offered for the train.
In New Zealand, Christchurch Airport is served mainly by many local buses, but it is not possible to buy the local smartcard at the airport so you must pay $4 by cash only (change given) for a 2 hour ticket. With the smartcard, it's $4 for a day ticket. Personal registration is mandatory for the smartcard, which also expires after 3 years of non-use, so anyone visiting less frequently would need to do this every time.