The problem is we want to kill them, while in human body, without causing too much detriment to the host.
To do this, we essentially need to develop something that will cause serious harm to the bacteria and yet not harm human cells. This means exploiting various differences between bacteria and humans.
A polymer that kills cell walls indiscriminately is hardly an acceptable solution for a human. Yes, bacteria may not be able to gain resistance to it but also it can't ever be used on a real human because mass cell death will cause too much damage to the human.
And "solving the problem of selectivity" will cause bacteria to be able to find their resistance eventually. Because if it is possible to escape your cell wall getting disrupted because you have specific DNA -- a bacteria can gain resistance.
I am firmly of the opinion it is not possible to develop an antibiotic guaranteeing the bacteria will not be able to gain resistance to it.
Simply -- the resistance can be had as evidenced by human cells. And the genetic material is abundantly available to the bacteria -- they are pretty much surrounded by it while in our bodies. There is always going to be non-zero chance for resistance to be acquired by a cell and then spread to the offspring.