I would like to live in your idealised world
Not sure an opinion on what should or could happen is idealised, I didn't say it would.
The path thing again by the way... What other use of a non-stop path from Paddington to Heathrow do you have in mind?
(Before you say HEX but government run remember that the government could charge what HEX charge and bring in money for the taxpayer, so anything less is a subsidy by any other name)
A cheaper HEX service is physically possible though. That is in my opinion what the service
should be. The government
could also unfreeze fuel duty to bring in money for the taxpayer, or change Avanti prices to result in a similar premium to Hex as there is the slower LNWR option. A cheaper HEX is exactly what the TfL report that the original article referred to suggested.
The government is not going to tell Heathrow to reduce the price. Heathrow would offer to reduce the price in return for a subsidy, as any business would. The only way the HEX would be cheaper is with subsidy.
The government absolutely could do many things with this. Heathrow is wanting to build a massive new expansion, which is also what this report was referring to, that gives a lot of leverage for the government to make them add in measures to reduce impacts on local communities.
As it stands the Elizabeth Line copes with Heathrow passengers, but at peak times for Heathrow it can causes issues closer to London for local passengers to get on. Heathrow wants to nearly double passenger numbers. The Elizabeth Line simply won't cope with that. Given Heathrow is a private entity standing to profit hugely from the development they do need to contribute to the effects it will have on services around the airport. Giving up its Heathrow Express is not a stretch and is a tiny drop in the water compared to volumes of money talks about with the expansion.
I would also note it isn't as simple as people can pay more for the quieter train, because the negative effects of poor use of the path are felt in the suburbs of and central London, where people can't get on trains because of people going to Heathrow, while the Express ferries empty seats.