FTP is failure to wait in most cases and often that means failure to wait for real labor. Inductions are so common that it seems to have slipped our minds that they fail a large portion of the time. It's difficult to make the body give birth if the baby isn't ready. I really hate that 'diagnosis' when used to justify a c-section because it's so rarely true. Yes, you are correct that induction is a primary cause for this issue. The c-section rate skyrockets with induction and it's not just due to the cascade of interventions (extra pain = epidural = slower contractions = more pit = fetal distress) but it's also often due to the labor not getting anywhere because the mom was never in real labor.
Another reason for failure to wait is those cases where it is a normal labor pattern *for that woman* due to a variety of factors, but it is not within their acceptable limits. In these cases, it is not usually immediate risk to the mom or baby that motivates the c-section, it is fear of liability should something happen and they were seen to be doing 'nothing'. In our court system, taking action is always seen as more responsible than not taking action, regardless of the risks from that action. I think this idea is deeply rooted in our male-centric, medical system which views the female body as abnormal and as inferior incubators because they cannot be controlled. Regardless of the reason, however, c-sections are the gold standard of responsible care. Let me be clear that this is not because they are safer. C-sections carry significantly more risk for the mother than vaginal birth (about 4 times the risk of death) and a host of other issues for the baby not to delve into the long term consequences of motherbaby separation, breastfeeding difficulty, repeat cesareans, and the trauma to the mom.
As long as the hormonal balance of the mom's body is not being disrupted (this requires her to feel safe, private and unobserved), and she is well nourished and hydrated, and baby is handling contractions well, I see no excuse to expose them to the added risk of surgery. Long labors can be difficult and exhausting, but the truth is that a long labor that started naturally and progresses on it's own time, in which the mom is well cared for and comfortable in her space, is a completely different situation from a long labor that involves prostaglandin gel, water breaking, pit augmentation, epidural, constant fetal ultrasound (heart monitors), and laying in bed on your back.
As far as the baby not dropping, the concern is that there is some physical reason for the baby to not descend into the pelvis. However, it is incredibly rare in the US for a woman to have a pelvis that cannot birth her baby. The system is just designed too well for that. Without nutritional deficiencies that warp the bones, or serious injury that has messed up the flexibility or shape, almost every woman can birth the baby she grew.
I am speaking in generalities here because that's all you can do with a little information on the internet, but I encourage you to try to find a midwife who trusts birth to work, and who doesn't feel the need to follow strict medical protocols. Then I would stay home to give birth.
If you don't want to consider home birth, I highly encourage you to refuse any kind of induction and wait for true, active labor, before going to the hospital. I also want to give you hope. The rate of vaginal birth success with hospital vbac is pretty high if you actually get to the point of labor (many women are promised a vbac but are pushed into a cesarean or an induction which raises the rate of cesarean at the end of pregnancy regardless of what their Dr. promised them). In fact it's higher than the chance of vaginal birth overall considering the national cesarean rate.