Joe'smom --
Always a good discussion
Shortest form I can manage is we each have our own expressions of scrap quilting. Random is one component but not required. I generally have a rule set for each project such as no more than 8 uses of any given fabric, or whatever it might be. I'm happiest making identical (usually "traditional") blocks in different fabric sets, where each fabric for each block is indeed carefully chosen and sometimes even fussy cut.
I'm lucky enough that mostly I make quilts because I like to make quilts. Really, mostly I like to piece and find quilting down a necessary evil, but I'm working on that. Without someone in particular to make a quilt, my choices of design and project can be based on something from -- it's time to do something with that pansy fabric or gee, that purple box is getting pretty full. Or, you know, it's been awhile since you did any set-in corners, maybe you should improve your skills.
I like using these Bonnie Hunter projects as chances to use up small pieces. Sad to say, some of these are 10" squares I got from fabric swapping back around Y2K!! I can follow her directions and trust that it will work out in the end. I don't have to worry so much about perfection in a mystery quilt (I fully understand the folks that don't want to commit until they see the final reveal!). There are going to be some homely faces and maybe a double ugly in there, but when you put it all together (with a little luck) it's all fine.