Caution: Nature's headline is deceptive at best.
Zero human hearts were involved in the research - instead, it was tiny samples of derived-from-stem-cells cultured heart muscle cells. Plenty of concerning changes were observed in those cells, compared to the control samples (which stayed on Earth, instead of spending a month in space). But the researchers were honest about the limitations of their study - it's extremely early stage, useful only for getting some ideas about what things might be worth a closer look.
This is very interesting, but I wish the article did more to offer some common hypotheses on exactly why this happens.
Is it out of fashion or are there other reasons not to use animals?
I think it is because lately humans are considered animals as well, and at least those can consent to such experiments.
Speculation: Doing live animal research in space is far more difficult, expensive, and laborious than doing any sort of "cells in a petri dish" research.
I flew to California for a month and when I returned, the cardiologist solemnly informed me that my heart had aged over 30 days! I said "doc, that's horrible, why do you think it happened?" and the doctor said that treatment wouldn't be covered by insurance, because it was my fault for choosing to travel slower than the speed of light. I'll never do that again!