The problem is that her notes reveal that her parents were mildly prosperous and could possibly have finessed their way into getting at least one of the creature comforts to shut her up and make her stop yowling about how everyone but them was rich. They simply didn't want to because they didn't trust the post-war prosperity to last and also, they had no immediate use for all of the crap she wanted to get because they played a longer game than she ever did. Since I AM Lynn's 'kind', I know how they managed to do so and put aside money for better, more useful purposes like putting her and Alan through post-secondary education: they used the simple technique of declaring that anything that they didn't feel like buying was magically really expensive.
Since Lynn is a baby-boomer and thus kind of dumb, she took that rather obvious lie at face value and sincerely believes that she was deprived and thus requires that people mutate into vending machines to make up for fake, no-way, impossible impoverishment. Since Shit Stupid John and Thinking Impaired Elly are both her, they have to own horses because they both want to make up for artificial deprivation and to punish children for taking things for granted.