I have no special knowledge of Cross Rail 2 and no view on this particular project either way. It is simply not a subject that has even crossed my radar before but I have some general views.
My first response was that I wasn't aware that MK actually used public transport and that, if he did, his view might be different. I guess that none of the people who can afford to own property in "London's richest borough" actually need the public transport services that the rest of us need and use. What of them? Those who work for the rich people? Or provide the services that they need and use? People who may not live in "London's richest borough" but work in offices there? Or those visiting "historic Chelsea"? Are the needs and views of all these people being sought? Would they not find a new train station in Chelsea of use? I have no idea but London needs both to improve and to increase its public transport infrastructure - of that, I have no doubt.
I come from West London - born and bred - but not the "posh" bit. Though I haven't lived there in a while, I visit not infrequently. I speak as a Londoner who has not only lived there but also studied there and worked there. I may have not welcomed all of the changes that have transformed London from the place of my youth but I recognise that London has to change. The public transport system used to be really busy in the rush hour periods but much less so at other times (particularly at weekends). Nowadays, it is busy most of the time.
Additional facilities (including new rail lines and new stations) are needed, as well as the renewal and/or development of existing facilities. Chelsea, however rich or historic, is not an exception. Only some new, as-yet-unknown, technology, that totally changes the way we live and work, transforming the patterns of our lives, is likely to render that need irrelevant. It would have to be a change as significant as the coming of the railways in the first place, a century and a half, or more, ago. Other than that, London has no choice but to invest in its public transport.