If you understand the lifecycle of headlice and have infinite patience, they are actually quite simple to eradicate.
Getting headlice is nothing to be ashamed of. Getting infected repeatedly is nothing to be ashamed of either, since unless everyone is treated at the same time, the likelihood is quite high. However, having a child who is crawling with them IS a sign of neglect IMO, since to reach that stage the problem will have been ignored for some time.
Where most people go wrong is relying on chemical solutions/hair treatments to kill them. They mostly don't work and you still have to comb anyway to remove dead lice and eggs. This is the part most people don't do thoroughly enough because they view it as cosmetic (removing the debris) rather than a vital part of treatment.
To comb a head properly takes time. The hair needs to be divided into no more than inch-square segments so you can get the comb right in at the scalp and remove everything. A child who has long, thick or curly hair can make the process even longer. It's a complete PITA and I can well understand why people fail to do it properly, especially if they have more than one child, job, other commitments, etc. But it remains the truth that this process, done thoroughly every other or every third day for about 7-10 days, will eradicate an infestation. While you may miss a few eggs no matter how careful you are, the repeated combings over a week or so catch the ones you miss.
FWIW, tying back hair makes very little difference since lice rarely travel up and down the hair's length; they stay close to the scalp where it warm and where they can feed. Transfer takes place when heads are touching, which is why the problem is much more intense at infant/primary school, where much more close contact occurs between pupils.
Headlice are also very hard to dislodge from the hair (hence needing a good comb like the nitty gritty) and hardly ever fall off unless they are at the end of their lifecycle and past egg-laying. Catching them from brushes, hats, pillows, etc is unlikely.