I was under the impression that the Cockroach King was purely a metaphor for capitalism in The Mountain
That was my impression on first listen as well. Chasing the capitalist dream and getting close enough to see the cruelness and merciless nature of it.
But then if you're a capitalist; you'd probably be able to see it as something else that fits your world view better and that's kinda the beauty of it all, being open to interpretations.
(a concept album without a direct story, about dealing with success & the aftermath of it).
I'm not sure if it's specific to Roger Waters, but he calls these "thematic". Like DSOTM, WYWH & Animals, unlike The Wall which does have an actual plot.
It feels like The Path gives us an overview of what the album is about, pretty clearly too IMO.
This life is a dream
A gift we receive
To live and to love
We forge The Path
Our nightmare in birth
Our struggle for worth
In vain we carry on
Our mission to become
Adapt to this world
It's a chance we must take
We'll sing our song
We'll play our hand
So, to me, this reads like all the topics the rest of the songs cover. Life is beautiful, we're meant to use it to give and receive love without being passive, but it's not that simple. There are immense challenges in the way of doing so, primarily; having to engage and adapt to the world without letting it drag us away from life's initial purpose (to give and receive love). So we try and give it our best shot, but there's also emphasis that luck plays a role.
Taking the time to go over the booklet a bunch of times over the last couple of days; I cannot help comparing this album to The Dark Side of The Moon, an album commonly described as being about "how everyday pressures of modern life can lead to madness", although I don't fully agree with that common assessment. Not the same exact theme as The Mountain, but as close as any other work would get to it, thematically that is.
And to stir the same emotions that DSOTM did to me, to even make your album comparable to DSOTM to me, is such a monumental fuckin achievement if I may say so. Fuckin bravo Haken.
I'm not sure about capitalism
But certainly it's about greed and ambition.