oksewglad, sews with tiny squares like this. Hopefully she will come comment on your question. Here's a link to her profile. In her albums, she has pictures of her mini's.
https://www.quiltingboard.com/member...lad-u7338.html Here's also a link to one of her specific photos, it really shows the size and scale of the pieces she uses.
https://www.quiltingboard.com/member...56-323777.html
I don't know why you can't use these squares up. Maybe a long term project or a smaller project. As it will take a long time for 1" squares to amount to something.
But, where there's a will, there's a way.
I hope you find the encouragement you seek.