Labour demand. Moscow used to have lots and lots of factories and these factories needed workers. Increasing industrial capacity was seen as more important than providing every worker's family with their own flat right now, so stopgap measures like communal flats, dorm-style flats, hotel-style flats were used. Some are occupied to this day by people waiting for their proper flat since 1972.
This puts the Moscow Metro bomb shelter efforts solidly a decade later than London's conversion of Tube stations into dual-use bomb shelters, which started shortly pre-nuclear as a response to the unique challenges of defending London from the Blitz (London was highly dense and radionavigation was coming into use, largely defeating blackouts as a damage control measure). The United States made various runs at similar projects from the '50s to the '80s but they never got particularly far (which is a statement that goes generally for US civil defense efforts), probably in large part because the US never actually faced bombing like Great Britain had.
The English experience was very well-understood by socialists and communists (Marx and Engels themself had kickstarted their efforts in Manchester, after witnessing - and arguably exploiting, given their ownership of factories - the terrible conditions of the industrial working classes). It makes sense that proper housing would have been at the forefront of the industrialization efforts in the USSR, to avoid ending up in those same conditions; but industrialization itself was being pushed at breakneck speed, forever negating any progress achieved on the housing side. Hence a perennial state of "we should do something about housing!!"...
Marx never owned any factories - if anything he was near permanently destitute and often living off handouts from friends like Engels. A lot of his correspondence is complaining about money problems - often to Engels.
Engels family owned factories, and in fact his father sent him to Manchester to work at one to try to get him to turn away from his radical ideas, but which appears to have had the opposite effect. At several points his family basically threatened to cut him to try to get him to stop his political involvement, but kept relenting. You're indirectly right in that Engels certainly did profit via financial support from his family, and eventually, a few years before retirement, reached partner at the Manchester factory of the family firm.
That applies to the oldest stations in the city's center. Many stations build even in 1980s are not so deep & suitable for the task, though they may have some special means integrated too.
To the other points raise, I never quite understood the multi-decade Moscow housing shortages. The USSR (and now Russia) had internal travel passports, and at least back then you couldn't just pick up your bags and move to a different city. Why were more people than houses allowed to immigrate to Moscow? Maybe someone has some historical insight into this?