The Olympics brings in lots of revenue and counting medals is just one of those things. The local economy benefits more than anything else. This is shown by how many bids counties throw at the Olympics. If it didn't matter they wouldn't bother. The medal count is just a way of keeping morale up and people watching. TV ratings alone should justify the time spent.
The Olympics is the most popular sporting event in the world, and any funding spent to pay for a program involved in this is appropriate. These programs are important to keep the Olympics going like it is, and anything in place today needs to keep going, since the Olympics is a successful event.
Olympic funding isn't a problem because of all the money it generates. Millions of people benefit from the Olympics, and a lot of jobs are created every four years. As a matter of fact, if we had an olympics every 2 years instead, it would be a boost to the world's economy.
While olympic medals are a source of pride to participating countries, funding olympic sports in order to make a good "showing" is inappropriate in these difficult economic times. Using money that could be spent on education, infrastructure, researching new energy sources, etc. should not be allocated towards a few individuals who participate in fringe sports such as bobsledding and speed skating.
Olympic medal counts are of little value beyond providing a level of pride to the countries that achieve high medal counts. We should instead provide funding towards more meaningful metrics such as medal count per-capita or medal count in relation to a countries Gross Domestic Product (GDP). The media tends to over-value medal counts in countries where high medal counts are already assured (such as the United States, Canada, and Russia in the case of the Winter Olympics).