They are now late teens and couldn’t care less about this stuff. No way would I be hoarding random toys because they might get upset when they get older and they don’t have the rubber duck they used to take baths with, or whatever. I don’t think it’s good to be so attached to stuff.
That's them, though; other people see things very differently. There was a recent thread where OP had been given about half a shoebox-full of cards that her parents had been given on the occasion of her birth and baptism, and she wasn't bothered about keeping it - although she still decided to start a thread about it, which suggested that she wasn't 100% certain. Some people agreed with her and others (like me) were horrified at the (personal) thought of throwing such things away. However, whatever she did, it was her choice as an adult to make.
Obviously, you can't keep absolutely everything, but plenty of us do appreciate and greatly value the memories of a few of our old precious toys and childhood possessions, especially when our parents are no longer with us. You don't always even know yourself what particular items might bring loads of beautiful memories flooding back when you're 40/50/60/70/80/90.
I think we do children a huge disservice if we just throw out or give away their possessions without their knowledge and clear consent. At 3 and 7, they haven't bought any of those things themselves, so it becomes presents that loved ones (mostly their parents) have given to them and are now taking away again. It can indeed cause enduring trust and attachment problems if they learn that, as well as the naughty children in the park who might want to steal their bike, they can't even rely on their own parents not to (as they might see it) do the same, with their things in their own home.
I also think it's unfair to just give them a box and say they have to fill it with stuff that they're going to lose for good (no problem if it's safely in storage and easily retrievable). Would you do the same with your own goods? You might look at a great big oak wardrobe and decide that you'll have nowhere to put it in the new place, so it needs to go; but how would you feel if somebody told you that you had to look at the furniture and your other goods and lose an arbitrary quarter/third/half of everything you own?
How would you feel if your DH gave you a wodge of black bags and told you that you had to choose which half of your clothes to keep and bag up the rest for charity, 'because you've got too many and you can't keep them all'? As for just doing it without your knowledge, again, what if you got home to find that your DH had 'sorted through' your wardrobe and got rid of the 50% of your clothes that he 'didn't think were your favourites'?
There are cases where children need to be strongly encouraged to make the 'right' decision - and if something becomes dangerous for them, you might have to step in; but they aren't possessions or extensions of you - they're individual people in their own right, with feelings, emotions, personalities, worries, concerns and countless other needs and characteristics, just the same.