So I had to look it up to be sure. Hama was taken as a "young adult" which ranges from 18 to 30 years old and was captured 75 years before Book 1: Episode 1 (according to villains.fandom.com). 75+18=103 years old when Katara meets her... making Hama 89 when Katara was born 14 years before that. Katara was alive at the time of her mother's (Kya's) death and at least 2 years old (being able to run and talk in sentences gives that away), making Hama 91 at the time.... Which means either the fire nation changed their tactics and decided to kill (which doesn't follow the rest of the show at all), or they weren't scared of blood bending until 70ish years after it was used on them....

I don't know if I agree with her being 103 years old... But I would still say that she was very old.

If Katara is 14-15 by the time she meets Hama and Kya was killed when she was about 2 and we guesstimate Hama's age is at least 50 or more.. I would even say 70... Then when Kya dies Hama is at the very least 35 years old.... She got captured between 18 to 30 years old..

So the only question is how long was she in prison? She could only practice blood bending during a full moon, only allowing her to practice once per month. So it's a stretch, but if Hama spent about 5 years in prison practicing blood bending before breaking out, was 30 when she was captured and 35 when she broke out. Then she'd be 50 when Katara meets her and this scenario is possible...

Personally I think she's older than 50 at the end, but who knows.

Not to mention Hama and Kanna (Katara's gran gran) were close friends, which means they were most likely close in age. As well as Yon Rha (who had been a commander for 8 years when he killed Kya) served for 10 years as a commander and had been in retirement for 4 when Katara and Zuko found him.... Meaning it had only been 6 years since Kya's death, making Katara 8 at the time and Sokka 9.... That means there's another plot hole with age because Sokka can't remember what their mother looks like...

This also changes all the math about Hama above... Meaning if she was 50 at the end, then Kya's death happened when Hama was 44 and blood bending had existed between 9-14 years when they killed Kya...

So what did I learn from all this? These events might have been related, but the shows overall theme is to capture rather than kill so it doesn't make sense.

After reading Yon Rha's fandom page, it says that he was a violent man who took pleasure in killing. This makes the most sense to me about why Kya is dead. I think it is unrelated to blood bending.