Is it really a problem to be solved? As the article mentions, there's no negative association with the word tsundoku in Japan. It seems like having a reserve of reading material is a good thing; you'll always have something new to read and learn when you * do * have unexpectedly free time. The material will be pre-filtered to subjects you care about and it will be close at hand, minimizing the friction of using those random gaps.

I guess one downside is queue prioritization and management, but maybe the piling gives you an opportunity to test the strength of your interest in a subject relative to other items in your queue.