Rats are great for children, but primarily as "family" pets. A family should adopt a rat with the same considerations they would adopt a dog. A child can assume some responsibility, but a responsible adult needs to oversee the care and be committed to ensuring the rats' needs will be met.
As a member of the very popular and informative Goosemoose Pet Forums, my heart breaks whenever a young person posts that their rat is sick and their parents won't take him to the vet and they don't have any money or transportation to do it themselves. They are desperate for a home remedy that doesn't exist and heartbroken that they are on the verge of losing a friend who could be saved, but powerless to do anything about it.
Sometimes these posters are told a harsh reality, that they never should have adopted a rat if they didn't have the means to care for it properly. Salt in the wound. True words, but they are young. They didn't know any better. It is a hard way to learn a lesson and both the child and the rats suffer for it.
This is not necessarily a failure of a child, who doesn't have the world experience to have made better choices. This is parenting fail.
Parents want their kids to be happy, and kids love animals. It seems so simple to buy them a pet store cage and an inexpensive critter, and let them feed it and clean up after it until it lives out its natural life. Many parents are of my generation, and when we were kids, there were few vets who saw small animals. Pocket pets were cheap and replaceable. They got sick. They died. There was nothing you could do about it - it was just life. They got replaced with another inexpensive animal or their owners moved on to something else. There was little veterinary research being done on proper care and treatment of these animals and their diseases, so veterinarians were of little help in treating them, and so no one brought them in to be treated. There was no money to be made in conducting the research or in training to treat them since there was no demand for veterinary care for these animals. Replacing them was cheaper than treating them - the value of the animal was no more than the price initially paid for it (a silly conclusion when you think about it, since food and housing will instantly eclipse the price of the animal and no one thinks twice about that). It was a vicious circle leading to nowhere, and many parents who grew up during that period do not realize that things have changed.
Today, there are many vets who see exotics and small animals. Some are more experienced than others, but often the less experienced can treat the simple common problems just fine and then refer you to the specialists for the more advanced problems. The value of a small animal is no longer limited to its price tag. It is a life. It is precious and irreplaceable. It loves us and we love it. "It" is no longer an "it," but instead, a "he" or a "she" and more so "family" and especially a "friend."
The parenting fail happens when parents don't do their homework. Once, information about small animals was confined to petstore books that were brief and often wrong. Now, there is an Internet full of information about any kind of animal you might ever want to bring into your home. There are whole communities that have sprung up around these animals, with active forums where we can all learn from each other. Before allowing any child to bring home a pet, an adult needs to spend a little time on the Internet, learning about the needs of the pet, and deciding whether or not he/she can take on those responsibilities. Because if our children do not have the financial means to meet those needs or the transportation to get to a veterinary practice or the maturity to live up to their responsibility, then the parent needs to be willing to provide these things - or they should not consent to bringing home the pet.
So how does this apply specifically to rats?
First, rats are prone to many health problems. They already have a short lifespan, usually 2-3 years, but that can be cut even shorter without proper veterinary care. In our home, our rats need more frequent veterinary care than our dogs or our birds. They are prone to respiratory infections that must be treated with antibiotics that can only be provided via prescription from a vet. With proper treatment, the rats can live long happy lives while managing chronic respiratory problems. Without proper treatment, they will suffer and die prematurely. They are also susceptible to tumors, some of which will require surgical removal. Children are not always aware of the signs of illness and they usually don't have the veterinary access required to treat such problems. An adult needs to oversee the health of the pets.
Second, pet stores and pet supply manufacturers are either very ignorant about the needs of rats or they make decisions based on what will sell and not what the rats need. Specifically, cages and diets marketed for rats are frequently inappropriate for them. Most commercial rat diets are not balanced for rats (with a few exceptions). Most cages labeled for rats are too small and they are often difficult to maintain. But a child, on his or her own, will likely rely on what the pet store employees erroneously tell them is good for a rat - like a small cage and a bag of seed and nut mix. An adult needs to actually research the needs of a rat and decide whether or not they can afford an appropriate cage/diet/environment before adopting a rat. Appropriately sized cages tend to be large - space in the home needs to be afforded to such a cage. A small cage located on a bedroom night table won't cut it.
Third, rats are very social animals. They need time out of their cage every day and social interaction with their humans. This is a great responsibility for children to take on, but children can be very active and might not always be able to commit some time to their pets - school, sports, musical instruments, hobbies, and friends all make demands on our children's time. And children often tire of their responsibilities - what once was novel and fun has over time become dull and boring. Thus, it is good for our pet rats to have an entire family to fall back on. When one person has a full schedule, someone else can step in and make sure our ratties get some love and out time. And if everyone in the family wants to love on the rats - so much the better - you can't give them too much attention.
Finally, since rats need out time, a rat-safe environment needs to be provided for them. Someplace where they can be confined and kept away from the dangers in the house. Someplace where they cannot chew on electrical cords or damage furniture or mark the carpet (unless you plan to clean the carpet often). A child is not the best judge of these things.
And if your child wants a pet that is solely his/hers rather than a family pet, well - if they are ready for that responsibility, give it a go, but be there in the background in case things don't go as planned. As long as you understand these animals are, at heart, your responsibility, there is no reason that your children have to know that.