I do a lot of crafts and sewing is one of them. Before I discard any clothing, I mean actually throw them away, I take the time to snip buttons and rip out zippers that I find useful for future sewing projects. Some may think this is a bit much but even so these items are not going to reduce in cost. Even shoe strings from old tennis shoes, if in good condition, are worth keeping.
I do the same as you do. And I'll even repurpose the material from the clothing if I can, for example if it's a T-Shirt I can use the bulk of the front and back of the T-Shirt to cover a cushion. Even the sleeves can be used as cloths. I make sure not to waste anything as it can all come in handy. I've got several pots of old buttons sat around, and a collection of zips and shoe laces too. I also keep the snaps you get sometimes on coats as they can be reused as well. I suppose for some people it might be going too far, but I'm with you in that it's useful to have all of those sorts of things there for when you need them for repairs. Buttons can also be made into quite nice bracelets for kids if they're big and bright!
The thrift store near me does that. If a piece isn't suitable for selling, they save the buttons and zippers and stuff to resell, and they sell off bulk cloth leftovers to a nearby company to use for rags. Nothing gets wasted, so yeah, I think it's a great idea. I'd definitely save that stuff too. Have you seen the prices of buttons lately? I can't remember the last time I actually threw away a piece of clothing. Well, maybe after it had already been turned into a rag. If it got used for working on the car and was greasy or something, yeah, then it's going in the trash. Still, it ended up getting at least one more use, so it really wasn't wasted. Waste not, want not.