Even in the US, I don't know many friends with enough living space to have an entire spare guest room. When friends visit, they sleep on the living room couch or an air mattress. Is this not typical?

Flippant answer: in the U.S., in your twenties, you have no spare space, and visiting friends sleep on your couch. In your forties, you have a guest bedroom, and visiting friends stay at a hotel.

Possibly more accurate answer: it depends on what kind of housing people live in, if they have kids, and if they work at home. Most residential houses were built for couples with children, so if someone owns a house and is single and/or childless, they likely have spare bedrooms that serve as a home offices, hobby spaces, or guest bedrooms. People living in apartments usually don't pay for more space than required for their daily needs.

I think the operating word here is not "mattress" but "kitchen". How cramped do things have to be to need to put the guest mattress in the kitchen?

Somebody else was likely sleeping in the living room already. The reality of living conditions in the USSR was harsh.

You were typically allocated spacious 9 square meters (96 sq. ft.) of living space per person, with an additional 18 square meters for the head of the family. So a 4-person family would get about 45 square meters (485 sq. ft.)

And these were _typical_ numbers, not a guarantee. Plenty of families had less space.