There is no market failure, market is a combined desire of individual participants. There is market manipulation by governments. Governments that stand in the way of companies trying to bring products to markets.
IF there is such a huge need for antibiotics people should be able to make money by satisfying that need and if that means that a large amount of money first has to be gambled with, it's possible to achieve even that by raising that money in the free market the way kickstarter does it.
Of-course there is no free market in drugs, government is all over it, so don't talk about 'market failure'. There are perfectly valid FREE MARKET solutions to it, but the government PREVENTS free market from existing in the drug industry. You could start a company tomorrow and try and create new antibiotics if government wasn't standing in your way and all you would have to do is start a money raising campaign for that purpose. Try it, see how fast the government stops you from doing whatever it is you think needs to be done here.
But instead you want the slave owner State system to steal money from people to run your pet project and you want most of that money to be stolen from people who have more of it than you do, thus 'progressive income tax' and such.