I strongly object to your somewhat generalised statement about rural locations having a passable public transport offering. Counties such as Cheshire East have had no compunction whatsoever to taking the proverbial axe to subsidised bus services over recent years that once served local villages and hamlets. Many elderly residents of these areas would not take kindly to your suggestion of cycling, especially in heavy rain showers or when the snow lies on the ground "deep and crisp and even".
I didn't say that every rural location has a passable public transport option, I said a good proportion of the 15% population which live in rural locations (i.e. those places with the larger populations would have likely have passable public transport and for every place with 9,000 people there's got to be 9 places with a population of 1,000 just to balance it, let alone make it so that there's not a good proportion of the population in rural areas with passable public transport).
Clearly that still leaves a lot of places which won't have passable public transport, however the point is that the total population who do have access to public transport is the vast majority of the population.
The fact that there's areas where that's the case doesn't stop that from being true, however it does appear to be that there's many who live in urban areas which use it as an excuse as to why there can't be more incentives to use public transport by there being more of a tax on car ownership.
As to with regards to cycling again I didn't say everyone, I said many. Again there often appears to be much made about what about old people, bad weather, etc.
However to get to HALF the average distance cycled (total distance divided by the total population) in 1950 we'd need to increase cycling rates by a factor of 2.4.
The reason I select the target of half is so to allow for the increase in average age over that timeframe. As such there is a lot more cycling which many could do but they don't because they'll rather drive their cars 600m than walk to take their child to school only to return home again.
The 1950's average was nearly 1.1km/day, it's currently 225m/day. With those current levels a few km at a weekend during the the summer months reaches that amount.
With the advent of e-bikes then the ability to user bikes for more travel should be made easier.
As to bad weather, that too is often over rated. With the number of wet days that even very wet places in the UK seeing is only about 1/2 the days. However even that isn't the full picture as several wet days only have very light rain, with several more will be limited to an hour or so of rainfall. As such the risk of actually getting wet when undertaking daily tasks is fairly low, even with poor clothing.
With reasonable clothing (I never remember who is accredited to but it's very true there's no such thing as bad weather just bad clothing) even very heavy rain isn't a problem to be out in for 1/4 an hour, whilst good clothing would extend that time further.
Of course there'll be those who won't be able to cycle, however in the greater scheme of the total population the overall numbers aren't going to be overly significant compared to the numbers who could do so and don't.