Driving in London is expensive and inconvenient. Parking is extortionate, there's the congestion charge, road taxes, fuel duty and insurance. A car is something you get if you're reasonably well off or you need it for work (e.g. you're a tradesman).
Travelcards are expensive too - London is just expensive unfortunately. But that's a Z1-5 travelcard I think you've quoted. There are other ones and IME a lot of very poor people cycle, use the bus pass (£900) or get a Z2-6 (£1800) then walk from there, if indeed they even work in the centre. Also there are discounted rates for the travelcard depending on circumstances.
In 2017, pre pandemic, there were only 166,000 annual travelcards sold.
No idea where your £2,568 comes from.