Another word for monument or idol?

Solution 1:

token

adjective — used to describe something that is done with very little effort and only to give the appearance that an effort is being made (Merriam-Webster)

As in: Rather than helping to solve the housing shortage, Stalin's skyscrapers functioned as tokens of an abstract socialist future.

Or: Rather than helping to solve the housing shortage, Stalin's skyscrapers were merely a token gesture toward an abstract socialist future.

Solution 2:

One synonym to monument that connotes worship, and that in my opinion reads well in your example sentence is:

Shrine: A place regarded as holy that is typically marked by a building or other construction.

"Rather than helping to solve the housing shortage, Stalin's skyscrapers functioned as shrines to an abstract socialist future."

Oxford American College Dictionary.