Barriers to infection such as skin, wax in ears, cilia lining airways, mucous, acidity of vagina etc. These defenses are always present, they act to prevent infection rather than combat infection. It does not adapt to any great extent, so if an pathogen finds a way around, theres not much which can be done.
Immune response, takes time for pathogen antigens to meet lymphocytes with complementary antibodies. Also takes time for cells to differentiate into killers, helpers, memory cells.... and takes time to produce antibodies. Becomes more effective over time, if the same pathogen invades a second time, it stands even less chance
EDIT: just seen you said immune response, so disregard my post :P
Non-specific are useful to catch pathogens at random, not only catching them before the immune response has started yet, but working to kick start the immune response themselves. In the case of phagocytes at least; with the more general non-specific immune system, as above, mucus and saliva and saline in your tears, are generally effective, and probably kill more bacteria all over, but aren;t much help when an infection actually starts, and you can die. xD Could be seen as the most efficient though, there is a lot of waste in the secondary immune system, and rather effective.
The problems with Phagocytes- there are fewer of them, they are not as efficient at halting infections? They don't mulitply rapidly, neutralise and even kill (Killer T cells) the pathogen, and ultimately, although slower, they eliminate the disease, or you die. ...That sort of works as evidence too that non-specific phagocytes can't eliminate a disease/infection on its own. So effective, but ineffiecient; the lymphatic system can be seen as more effective at ulimately killing the disease, and more efficient as it specifically targets the unwanted pathogen, by identification of the antigen glycocarbon/protein by the (variable region? Was that the name?) of the antibody.
Think of it like trying to catch a bouncing ball in a large interlocked maze, the ball splitting frequently into two and multiplying like something from 'the prisoner'. <3 You have a gun, that will not only kill it, but make a large bang, alerting others to the presence of the ball; however, you can not possibly shoot all the balls and deflate by yourself.
When you shoot the first one, you release a pack of small chihauhas, that steadily get multiply in number faster and faster, and round up on the balls, catching them or just biting into them to deflate them, some are bred with bigger teeth then others.
They keep increasing in number until you kill them all.
...had too much fun with that. xDD;;