Refugee camps aren't nice places, many are over crowded because they have too many people, many with the further cuts to FCDO and foreign aid, have had to shut down or don't have enough supplies. There is often just two tents, sometimes open to the weather, often people sleeping on top of rach other, mainly on the floor, which is the sand etc as they often don't have beds etc.
In fact the one set up in southern Mozambique in response to the recent burnings of the homes - the camp is running out of the supplies they use for children, they don't have enough money to get them all, they are asking for a rapid injection of funding but if they don't get it, some workers will have to leave as they won't be able to keep it going. Many charities/camps have been affected by the continued funding cuts of foriegn aid from the UK and other countries, the fact that many have done it at the same time has had disastrous effects.
In the recent attacks in Mozambique which are recent, the same ones also from Boko Haram in norther Nigeria, they burnt some of the homes and all people had (that's why they cannot get their documents, their were children having to flee and see decapitations, people took the clothes they had and ran, and tried to hide, many homes were destroyed, people were killed by Al Shabbah, and they forcibly displaced and moved these people out of their homes). This is very common in some these areas, both my terrorist groups, some of which are more powerful than the state, and in other areas by the state military as well.
With you saying many of these places expect you to carry ID, in certain areas if trying to flee, having said ID will mean you are caught, in many of these places as dictators etc get into power they revoke and take away people's passports etc as do many of the terrorist groups. In response to FGM as I also said it is a common tactic to inflict sexual violence onto men (yes still not FGM but that was just an example, I wasn't only talking about men in my comment). As I said earlier, Men in conflict zones are also victims of sexual violence, more than we expect. In the DRC, the UN has documented widespread cases of men and boys being raped in detention or conflict settings as a form of humiliation and control. Both my the state sometimes and often my such milita groups as well.
If you're escaping the sexual violence across Goma and the DRC, you are at risk of retribution from the military you cannot travel to your home (which many don't have any more), to get documents, you have to flee and do so as quickly as possible. Military forces, or militias often deliberately seize or destroy identity papers to control populations or prevent escape. For instance, Rohingya refugees in Myanmar were widely documented as having their papers confiscated, leaving them stateless, on purpose.
As I also said, men often gave the worse treatment (sometimes), with torture, forced military service, sexual violence as humiliation, worse punishments if they defy, or try to escape etc.
When you flee a country, you often don't pay anyone at that point (depending on geography), plus people smugglers approach them and exploit them. The crossing the chanel element is the last bit of the journey, so actually they don't contact them at the start. They often don't "cobble anything together", families often split up to avoid detection, men commonly go first as its a risky journery and then they try and bring other members over (they often travel behind, so they escape to another country and travel through, but the men tend to take the more dangerous path first, as it's easier to find ways to get the rest of your family into the safe country of your choice after). Many people leave with the clothes on their back, especially those who sometimes when they get to refugee camps, have to leave as its too full.
In respect to them staying in other countries or within they continent, the vast majority do, last year we only had 100k refugees and 34% were on small boats. Last year globally there were 43.7 million refugees.
Over 73 million people displaced within their own countries (internally displaced persons), so many don't even leave at all.
In terms of other safer African countries - The East of Africa hosted about 5.4 million refugees and asylum seekers in 2024. Whilst these same countries had 18.8 million internally displaced people. This means that refugee camps etc are very stretched, many people unfortunately cannot stay, and as I said above the cuts to foreign aid, has had a major impact as well, particularly with the specific food/pastes for those who are malnourished. Uganda for example took 1.8 million last year, Ethiopia, 1.1 million, etc.
In West & Central Africa, last year they had nearly 2.55 million refugees & asylum seekers (Chad, Cameroon, Niger, Mali, Nigeria, Côte d'Ivoire and other countries as well). The MENA region took around 16.6 million forcibly displaced people last year.
So Jordan around 611k, Egypt, 877k, Turkey 2.9 million. So in comparison to our 100k as a richer country and one with more resources in terms.of charities etc, is quite little as the countries nearby already do a lot. Unfortunately there's lots of bad things and conflicts, targeting, torture across the world and that leads to 43 million refugees and that's just the people who have to leave their countries and set up a new home.