But I think there're a couple of reasons for this:
first and probably the most possible reason is the song was written in September 1950, a little less than a year after China declare independent. So when CPC choose national anthem in June 1949, they won't be able to pick this song anyway.
So why we don't change the national anthem after? I actually asked my teacher when I was in elementary school, because I really dislike March of Volunteers, so depressing. I asked: it's peaceful time now, we're not "slaves who break free", we're not going to wars and die for our country, the song might have represent China back in the Sino-Japanese war, but not anymore.
My teacher, who's a really nice lady, actually answered my question instead of screaming "blasphemy" and punish me for it. I remember she said: I understand you probably don't like the song, and can't relate to it. It doesn't seem to represent us in peaceful time. But I think people choose this song because it represent our spirit, that we'll never back down, we'll never surrender against oppression, our greatest defense is indeed our people, that's why we say the new great wall is build by our flesh and blood, and we'll always going forward.
It was an unusual answer from my teachers who most of the time kept their distance and the longest conversation we had was about homework and school. But I really appreciate she took the time and explain it to me, treat me as an thinking person (not quite adult), instead of a kid who doesn't know anything.
Anyway, hope this answers your question.