Could you explain the case that TfL charges too low for fares due to a "socialist" mayor? Looking at the agency's reported recovery ratios, they actually recover more than 100% of their direct operating costs on the Underground from fares, and even buses have a 70% ratio. In the Western world this is actually abnormally high; in NYC buses don't even clear 20%. It's possible some of this gap is explained by accounting differences, but nonetheless London is clearly not charging cheap fares.

The reasons why Western systems often don't recoup even operating expenses, let alone capital costs, from fares are because transit is a public service with public externalities. Drivers on the road contribute to pollution and congestion, especially relevant in dense areas like London. Some level of subsidy is appropriate to account for the positive externalities of discouraging these negative outcomes while still encouraging regional mobility.

This is not to say TfL is as efficient as it could be; there is a well-documented capital costs crisis in the Anglosphere, particularly when it comes to transit. The issues here are more complex, though, than vote buying from an allegedly "socialist" mayor.

Since lockdowns I think the underground only recovers around 70% of its operating costs. Maybe you have seen different figures?

The freezes eliminated investment projects needed to keep pace with population growth. There's also just big problems maintaining the stations and doing more than the bare minimum needed to keep the lights on. Travel on it and the stations are dirty, overly hot, etc.

Drivers on London's roads are very heavily taxed already, supposedly to reflect those externalities. Public transport obviously also contributes to pollution and congestion, especially when building underground lines, it's not externality-free.

I don't think TfL has a cost crisis. Crossrail overran but that was mostly due to the software complexities of the signalling tech debt around the Heathrow tunnels and other issues that can affect any kind of project. It's just hard to tell right now because they can't build at all.

The fare freeze was broken by central government briefly, but only by bribing Khan with central government money for upgrades. Exactly the outcome he wanted!