I have watched that video 3 times, it goes great with morning coffee.
I know when we were growing up in our home my parents adored our animals/ foster animals probably every bit as much as they loved us, and if I were to be totally honest at times they loved them more

. We didn't refer to it as fostering, I am not sure if the term was common back then~ it was just an automatic way of life animals needed care, respect, love & compassion. I can't ever remember a time when our home wasn't the home that took animals in, nourished them, loved them healed them and opened our home to them or found them an amazing family of their own when they were ready. Mom and Dad came by their love and respect of animals from their parents. I truly believe people have the compassion or they don't. I don't think there is middle ground on this.
My daughter is 6 I had no doubt she would be fine with a chihuahua of any size, because I have no doubt she has it in her heart to care for and nurture animals. That being said we take precautions. But the precautions that apply to her apply to all of us. A little common sense goes a lonnnnnggg way and will get a person through many challenges/ obstacles in life. I am a realist an accident could happen, but an accident could be in the hands of an adult or a child. We don't carry the dog. We spend an unbelievable amount of time on the floor, lol. Yes there are times she gets scooped up by an adult but I don't permit any of the children she plays with to pick her up. That rule also applies to our cats, the bigger dogs & our fish... They aren't loved less, they cuddle with us on the furniture and snuggle/ play on our beds when they are ready, able capable, but we don't tote them around. Our house is childproof/ animal proof. She has an x-pen in the living room with a shower curtain down for her area. If she can't be 100% supervised (multiple sets of eyes mandatory for children, preferred for adults) she is in her x-pen (plenty of room for adults or kids to get in & play). She has her crate, an adult has to place her in it and remove her from it, because her little legs can get stuck in the door. All pet bowls, litter boxes are cleaned and dried each day and this responsibility doesn't fall on just one person we are all required to keep an eye out and do our part... We make trips to the vet as a family. The older kids realize its vital for their health & the expense involved, the 6 year old is learning, vet appoints are mandatory and do cost money. Usually people adopting an animal have a history that follows them with the animals in their life. Alot could be learned from that.
My brother's kids (ages 7, 5 & 2) have a little bit more of a wilder streak in them, they have larger animals in their home, the neighbor girl is 4 and has only known large breed dogs, never lived with a cat as her Mom is allergic. They all get to play with the kitties and the pup, 100% supervised to a much stronger degree than when I am with my daughter and she is having her supervised 1 on 1 time. When pup first came home they played with her, petted her gently and loved her while I held (protected) her on the floor. I explained about her tiny bones and her delicate, soft hair, her fragile "buggy" eyes, her little tender stub of a tail, her visible backside. From the moment they all met, they knew she was tiny, she was fragile and spending time with her required the kids to really be Big Kids and they were "responsible" to love her and keep her Safe. Even the 2 and 4 year old are able to learn to love & be gentle, and have done wonderfully as she grows. They are actually "proud" of themselves for looking out for her and being gentle with her. It's a process, but it's a valuable one for kids to learn be it with a Chi ~ who a responsible adult is able to protect and supervise under these times ~ a kitty, or a great dane.
If the adult is responsible their children have the potential to be as well. And you can tell a lot about the adult 1 on 1, and then when the adult has their children there, just watching them interact you can tell boatloads too. Each family would be unique, but there are families out there with children who are very capable of providing a safe environment for a Chihuahua.
On all the sites you can see rehoming the dog, doesn't like kids, can't train it, life "got in the way". It makes a person sick to read that over and over again. Shelters and Rescues are filled with animals because of the previous reasons, but a mind blowing percentage of those animals are a result of being homed with people who view animals as disposable objects of convenience. When the novelty and cuteness wears off and the the responsibility as well as expense kicks in ~ those cute little critters aren't so cute anymore and the baby that was loved and catered to (to a minimal degree in the grand scheme of things) is the victim of the most cruelest act ~ being turned away.
I would think some families with children could be considered, there are instances when it could work. But the person placing the animal would really have to go more miles than what they already do when placing an animal. Talking to the potential families and spending time with them and their children ~ you really could weed out the majority instantly, but there would be a few who you would know would put in their best efforts.
Our pup is safe, loved, cared for & protected even with a 6 year old in the home and real little kids in the family and friends. So I know it's possible. You would really just need to see a history & see the family in action together and talk to them in depth. It makes most sense to err on the side of caution, but I think you will find that every now and again a family with a child/children do meet and exceed expectations and have the ability and desire to provide a pup with the greatest home imaginable and in the end that is what you are looking for. If it happens 1 out of every 10 / 1 out of every 100 of family applicants is an amazing event.