Governments are voted in by the people and if these same people think that supporting horse racing is a waste of their tax paying dollars when the money could be better spent elsewhere it will be the people making the change by their votes.
I don't know where you live but, where I live the people vote for the Representative. The Rep. does what he/she wants once they have the position.
I can not recall one subsidy program that was ever discontinued because it was wasteful or unpopular with the voters. Can you?