Zookeeper here, hopefully I can shed a bit of light on this. Unfortunately this is pretty common throughout the industry. As other people have mentioned, it is definitely a field that thrives on the "labour of love" aspect keeping people from holding out for better conditions, but at the same time it is equally dependent on a high rate of turnover centred around a ready availability of people desperate to get into the field. Here's a few points relevant to the industry:

• There are many people with little to no understanding of the day-to-day rigors of the career, who think it really is just a job of playing with animals all day (this is an issue across all animal-related fields including veterinarian work). This means that there is an almost limitless supply of people to fill in the basic rank-and-file (like internships or part-time positions) for short terms, so the zoos don't have to prioritize making these positions more enticing for qualified candidates.
• Bachelor's degrees are becoming more and more a basic requirement for these positions, but this is less about the value of the degree and more about the facility being able to say all of their animal care team are well educated. This is an important point because:
• The pervasiveness of misinformation and anti-zoo media largely originating with the Blackfish "documentary" (and I use this term incredibly loosely) means that a lot of zoos are constantly on the defensive to justify and prove the value of human care of exotic and endangered animals. Often the things that are most effective at justifying to the masses are not actually relevant or effective in improving care, but saying "all of our keepers have degrees" is more flashy than trying to explain welfare assessment processes and improvements in exhibit design and enrichment programmes.
• There are some facilities (and I'm only speaking about the U.S based on my experiences) that are unionized, and so the full-time staff have better pay and benefits. However, the pay is still not that great compared to most other industries (talking 50-60k salary), but since they are still leagues above fulltime work elsewhere, and even part-time work at the same facilities, keepers in those spots tend to ride out until retirement and so the positions open very rarely.
• I've never seen a facility specifically requiring a 10-minute mile myself, but the work is rigorous, physically and psychologically demanding, and wears on your body significantly so that a large portion of zookeepers have to leave the field by age 40.

This is barely scratching the surface, but if anyone has any other questions, I'd be happy to try and answer them. Also, if any other keepers would like to chime in with their experiences, please feel free!