TGV doesn't make a profit by any normal accounting standards. As far as I know every line except Paris-Lyon has received large subsidies. The Bordeaux-Toulouse line requires a subsidy of 35 EUR per year per passenger for the next 50 years. Nor are tickets even cheap as a consequence. Supposedly it's cheaper to drive the moment you have at least two people in the car (I haven't checked that claim, probably there are routes where it's not true).

Rail in the UK requires subsidies. Once again you can play games with non-standard accounting, like by excluding the cost of track and stations, but those are the bulk of the costs. If rail subsidies were zeroed tomorrow every single railway in the UK would go bankrupt the day after. This is also true for the Tube which certainly isn't break even - where on earth did you read that? They were once able to cover daily operating costs from ticket fares, but Sadiq Khan put an end to that and now they can't even cover operational expenditure without subsidies from central government. Even back when they were able to balance the daily books they only achieved that by starving capital expenditure and not building up any kind of profit margin, meaning that any kind of upgrades or repairs have to come out of additional subsidies.

https://tfl.gov.uk/corporate/about-tfl/how-we-work/how-we-ar...

The Shinkansen has a long history of building unprofitable lines which led to JR's eventual "bankruptcy" in 1987, ending up 28 trillion yen in debt. After being semi-privatized they were given a lot more leeway to shut down their unprofitable lines, but even so, it's viable mostly due to the government ensuring they have access to nearly unlimited risk free and repayment-schedule free money (ZIRP).

Passenger railways are fundamentally not possible to run as ordinary free market companies. They were run that way once, but the railways were built out on the back of huge private sector investments in infrastructure. Governments the world over then nationalized them and redirected funds towards staff/union pay settlements or reducing ticket fares, cutting infrastructure spending to compensate. The result is a massive overhang of tech debt that now can't be paid off without unrealistically high ticket price rises.

British productivity is low because it has cheap labour due to effectively unlimited immigration. Companies invest in productivity improvements when labour becomes expensive, otherwise they don't bother, it's easier to just throw more people at a problem. None of that is really a secret, it just doesn't get talked about much because the British ruling classes don't like to criticize immigration lest they be called racist - however, this is a purely economic issue. Railways hardly matter for productivity and commuting may even harm it for many people, as evidenced by the popularity of working from home.