With the greatest of respect, that's a really silly analogy.
No it's simplified to make a point.
It makes no sense to have per capita spending on transport the same in all cities, towns and villages across the UK, because transport needs are different in different places. Suggesting that per capita spending on transport should be equal across the UK is as daft as suggesting that NHS should spend the same on every person - people have different health needs and thus spending per person varies according their needs.
That's the whole point of a nation state: everyone pays into a central pot - and spending from that pot is based on the need for various services.
Let's pick a public transport example. 14 years ago there was no tube station at Canary Wharf. It's now the 10th busiest station on the network, handling around 50 million passengers a year. But building it (and the rest of the Jubilee line extension) was a tad expensive - approx £3.5bn, or something approaching £500 for every man, woman and child in London.
Would spending that amount of money in, say, Manchester achieve the same 'benefit'? Bear in mind that Canary Wharf handles almost double the number of passengers as Manchester Piccadilly and Manchester Victoria combined. (Yes, I am aware they are different types of station, so not directly comparable - but it helps to give some perspective.) That's not to say that Manchester doesn't need spending on transport infrastructure (the Northern Hub improvements can't come soon enough for me) but the sheer scale of transport infrastructure requirements in and around London is staggering.
Also it hasn't helped that many big schemes were delayed for many years, adding to their costs. The
Thameslink Programme was originally called
Thameslink 2000 - that being the year it was meant to be finished, not the length of time it was going to take. Crossrail was being planned in the late 1980s/early 1990s.