As for comparisons with human sports, I agree with you, but there is a nuance: everywhere there is some acceptable percentage of deaths after which sport becomes unacceptable. For example, it was great in boxing before, and after the legislators ordered the boxing federation to fix it or close it, doping requirements and some rules were changed in favor of athletes. This greatly reduced the number of deaths in the ring (and out of it).
Now the important question is what is the actual mortality rate among racehorses and whether we can consider it acceptable to require a change in the format of the competition or something else to reduce it.
We have to accept that some animals are being used to make money. Some of them function that way not just because its necessary but tradition. Horse raising will always be a traditional game and it will never be banned because there will be lots of gamblers that will disagree. There are really unacceptable animals being used in gambling but we have to deal with it.
Yes, I do not see anything reprehensible to honestly admit that humanity uses animals for its own benefit (the simplest example is we eat them). So it was and so it will be, and this is due to humanism - most value human life and interests higher than the life of a chicken, for example. In my opinion, this is correct. I am rather afraid of the activity of those who want to equate human life with the life of an animal than the order of things that exists now.