I don't know a whole lot about the care system (most, though not all, of my "knowledge" comes from Cathy Glass books which are probably not that accurate!) but it's my understanding that children in care generally want to return home, whether that is appropriate or safe for them or not. And when they first come into care, I understand that the long term plan is often not at all clear; ideally, children will return home if that is possible, however this may not be appropriate or safe. Part of the foster carer's job is managing the child's emotions and uncertainty in the face of the fact that the foster carer themselves does not yet know what will happen to the child long term.
In the event a decision is made that the child cannot return to their parent(s), then there is often another period of uncertainty where the LA is making a decision behind the scenes whether to look at another relative, long term foster care, or adoption. In this situation I understand that it is common for the child to ask whether they can stay with their foster carer, and it is again the foster carer's job to manage this and the child's emotions about it in the face of the fact that they don't know where the child will end up staying long term.
It's my understanding that foster carers trained as short term (meaning the few weeks up to about 6-12 months as a PP explained) are not usually considered for long term placements although sometimes the "short term" placement can end up lasting several years. Long term is a different thing and I understand that in this model the carer is expected to keep the child from whatever age they arrive until adulthood. (Very short term care such as a weekend/few days up to a couple of weeks is called respite care).
When a decision is being made about where to place the child long term then, I understand the foster carer can make an application at this point, but the assumption is that short term placement foster carers will not apply for permanency because the idea is that they continue to foster other children. The children AFAIK are not supposed to be told who is making an application, they are only informed once a permanent family has been found. Of course it does sometimes happen, but the idea of keeping this quiet is that it prevents false hope being raised, if the child has a particular option in mind that they would really like but the court considers that a different option is better. The child is allowed to make their wishes known, but this will only form part of the decision, as there are often other factors which are more important.
OP I know people are saying you are naive and maybe you are, but I would guess that most people who eventually go into something like fostering start out naive and learn as they go. Nobody is born knowing everything and the care system is a bit of a mystery to most people. It would probably be best to go along to any local fostering info events - you should be able to find these in any area - and get some info from there because you have no idea if the info that's coming through on MN is accurate or whether people actually have experience in the field.
Secondly there are loads of "fostering memoir" books on the market, which are quite interesting in terms of showing what kinds of things foster carers might experience ,although I am sure they are not quite as true as the authors/publishers claim, and I'm sure many scenarios are painted with a much rosier ending than what probably happened in reality. My guess is that there is some accuracy in these books in terms of how the care system is structured, simply because it seems to match up with other info I've come across from other sources, although obviously they are written for entertainment not education. (Also being memoirs some will be based on older procedures no longer used).