Perhaps Apple has put more thought into all this than we give them credit for. The more I think about all these situations, they start to make more sense.
Purse/Bag/Keys/Personal Item Tracking:
If you are on public transit or in Uber or whatever, and the purse/bag remains near you, other people will not be notified since it is within range of the owner.
If you drop your keys behind a seat in an Uber vehicle without knowing and leave the vehicle, at some point the Uber driver, if they have an iPhone, will be notified they are being tracked. This will cause them to look in their vehicle for the tag (heck, maybe they will know before the owner knows they lost their keys?), and hopefully through that result, the owner of the keys can reunite with the Uber driver to have a happy ending. The Uber driver could also just toss them out in a park, and let the owner track them down that way on their own. Either way, end result is, owner gets his keys back.
If someone steals the purse or bag, yes they could dispose of of the tracker. You might find your tag, but you won't get your bag back. The most probably situation is that any items of value in the bag, likely will be take and the bag will be disposed of anyhow. Granted a thief could get notified they are being tracked and then they could panic and just put the bag down and run off, which would be a better situation potentially for getting your items back.
Car Tracking:
If you put one in your car and you are the only driver of your car, then no one will notified they are being tracked, since you are there, and they are riding along with you. If someone in your family group drives the car, they will get notified, unless they turn off notifications for family owned tags.
You will think twice about tracking your teen or spouse with one of these, without telling them there is a tag in the vehicle. While we can debate both sides of various situations, this is the most "healthy" method of tagging a car with different drivers.
If someone steals your car, if they have an iPhone, they will get notified they are being tracked. They could dig around and try to find it (if you stuck it somewhere easily found) but they may panic and then just ditch the car since they don't know if you are hot on their tail or clueless in Seattle. That likely is a better scenario than them not being notified at all. But if they don't have an iPhone, then eventually you may get your car back if it doesn't land in the chop shop.
Young Child Tracking:
If you are wanting to track your child and your child is going with someone else not in the family group, then you just need to communicate with the adult taking the child, that they have a tracker. Any adult would think this is fair and if they get notified they are being tracked, they will understand why. No big deal. If the kids is just at daycare and staying in one area, then it likely won't flag those around them with iPhones that they are being tracked (my guess).
If someone kidnaps your child you have a different situation on your hands. This might be one of the few instances you would want there to be no notification to anyone, but also finding the tracker on the child would be a pretty simple task, unless it is like hidden inside the sole of a shoe. But again, Apple is not marketing this as a method to track your young children.
3-Day Beeping on Moving:
This is to provide notification for people who are being tracked, who are not using iPhones. If you put it in a car and the driver is using Android, they will never know it is there. But after 3-days, assuming the owner of the Airtag hasn't been near that vehicle. it will make a noise causing the driver to investigate.
Just my thoughts on it all, I'm sure I have not even thought about all situations.