Bacteriophages are very much the answer to the titular problem. Instead of finding tiny little lethal molecules, we will likely end up actually designing machine-like phages to kill the causes of our illnesses. They're easy to select for, quite good at what they do, and are some of the most approachable objects in synthetic biology, currently. And they are much more amenable to continued use than the 3 or 4 scaffoldings of antibiotics (small molecules) that we know of today.
The biggest problem with phages is they can be quite specific. Antibiotics put phage research out to pasture because a single, easy to mass produce small molecules were capable of wiping out enormous varieties of bacteria.
With phages you'd need a large library to counter different bacteria, you'd have to successfully identify the bacteria which is causing the problem which may require culturing. If you wanted to maintain phage effectiveness in a heavily selected environment you'd also need to design phage "reactors" where the phages can be continually evolved against current bacterial populations.
Which in the long run is a far more elegant solution. Rather than "Kill All The Things!" (including your target), it's "Kill the Bad Guy!" - but you have to know who he was.
