Why was Brutalism so connected with public housing?

First of all defining trends in architecture is a tricky task. For example what you refer as "brutalism" based on those articles could be more properly classified as "brutalism-influenced" or "brutalist" late-stage or post-war modernist architecture (as opposed to early-stage pre-war modernism). During its heyday (mid 50s to mid 70s) brutalism was in fact a movement within the broad movement of modernist architecture. Back then modernism was still a movement, if a major one, and not yet the ubiquitous norm of architectural design. That meant that you didn't have "brutalist" neo-classical architecture or "brutalist" rustical country houses. Brutalism was an extreme form of modernism that quickly fell out of favour - within 20 years, which is very short for a building style - due to the negative effects being felt often by the same people who green-lit the design in the first place. At the same time a more moderate forms of modernism flourish and currently when we speak about "modern architecture" in the "contemporary" sense we mostly think of modernism or post-modernism (in all its variety, not just post-modernism proper)

So to answer your question you need to re-state it as two separate questions:

Why is modernism so connected with public housing?
Why is brutalism so prevalent in the design during that time?

To answer the first question - it is partly because modernism arose as an answer to the problem of providing cheap livable (or usable) spaces by reaching out to industrial solutions or functionality, mass-production and engineering rather than "artisting" your living space. It also became very successful at that and as a result it grew to be the main style in which public housing - by definition cheap and practical - was designed. Modernism was the first architectural style/movement that came with a comprehensive and increasingly scientific philosophy backing the design to the point where modernism in architecture can be considered the equivalent of the scientific/industrial revolution in wider society rather than just a distinct architectural style. There's a reason why the general classification has just two categories - modern and pre-modern architecture.

To answer the second question - Brutalism came out of the aesthetic idea of utilizing concrete as the main material to its fullest extent. There was very little in the way of practical thinking as evidenced by the poor state of the numerous public housing projects which are notoriously hard to maintain partly because of their terrible design and partly because of their construction utilizing simple concrete. It seemed very promising at the beginning because concrete is an extremely flexible material that can be used both as pre-fabricated elements and structures cast at the building site. People liked using concrete because of that and adding some aesthetics - even if controversial and questionable - seemed like a good idea at the time. It also seemed that the often poorly-thought out post-WW2 building rush would shape the way construction industry would function in the future and so the idea of huge blocks of cheap housing which now proves to be a disastrous idea in all but the most densely-populated places was presented as the solution to the crisis. At the same time the technology of concrete and casting/pre-fabricating it was very simple and so brutalism was the best people could come up with. And finally public housing projects were commissioned by public bodies therefore either attracting more "design-minded" architects rather the more practical commercial ones, or allowing the designers more design freedom. Often that resulted in design that was less than optimal for the end user as what works in real life and over decades of use is often very different from what works in a drawing or in a model during a presentation.

This is also why so many commercial buildings in post-WW2 Europe and so many new urban centres in boom-town America, including federal districts are "brutalist" in style - the same factors at play.