Here is a video of me soloing in Howling Stones, so you can see how much HP I lose typically. I made it very quickly and on the fly, so I could definitely do much better.
https://www.youtube.com/watch?v=WmDvk3udrhI
First three kills 00:00:00 - 00:06:00 show how few resources you can spend per kill with the right strategy and gear. If you maintain single mob pulls and keep track of the 20 minute respawn timer, you will barely lose HP, MP is the bigger factor. You can sacrifice some HP by using clickies to help mitigate MP loss.
The pull after that 00:06:10 - 00:09:50 shows double fear kiting. It wasn't planned, which is why it is a bit messy. I had to decide on the fly whether to FD or show a double fear kite. I decided to show the double fear kite, where you can have two mobs fear kited if you have a bad pull and do not want to FD it. I do not go below 50% health even here.
A mob is pulled after that 00:10:08 - 00:11:30 to show you can still do another kill or two on low resources before recovering. I don't lose much here due to it being a single pull.
Last pull was a bad one, but FDed just fine.
As you can see, at the end of the video I did not even dip below 50% health. There is no benefit to me stacking more HP here, as I still have at least 1.5k HP remaining before I take a med break. Increasing kill speed, however, will reduce damage taken, potentially save me having to cast a spell, and get more kills in per respawn cycle.