Isn't it unlikely that a naturally emerged virus would have both high virality and mortality rate? I have read that viruses usually have one or the other, which

Isn't it unlikely that a naturally emerged virus would have both high virality and mortality rate? I have read that viruses usually have one or the other, which would indicate that both is more rare. Combining the rare odd with the odds that the host happens to infect a human would make it even less likely to happen. I'm not very familiar with the topic so I could be mistaken. I don't think it's very interesting if it was a naturally or artificially selected virus. The more interesting question is was the infected specimen a research subject or not.