So, I went in search of some ideas on how to use them.
There's the obvious - build your layout on the sheet. This one is also matted on a small patterned paper (black polka dot.) I found this one in a simple Pinterest search. It's pretty straight forward and would easily fit more than one photo.
I also went to PageMaps in search of some ideas. I found this sketch. There's a layer on the left-hand side, with a scalloped edge, that could totally be a diecut sheet cut in half. If you like the straight edges found on the sketch, simply trim off the diecut edges, top and bottom.
I have done the cut-the-diecut-sheet thing, and sometimes I'm not always a fan of the decorative edge continuing along the top and bottom; there are times it just feels off. Sadly, I never thought to trim off the offending top and bottom edges. Duh! You can then use the trimmed off edges either as embellishments - the shorter scalloped pieces in the above sketch, or to make the "connection" in a two-page layout.
There are still some diecut papers produced today - Jillibean, for one, has a couple. The versions these days are more "lace" like, meaning, it's not patterned paper with a decorative edge. They are more like the Circle background in the above layout, also found at PageMaps. The new versions have numbers, stars, intricate patterns and words. These are easier, I think, to use. They are can be cut down without feeling broken -- trim out a block (like above) or even a row from a design like the above, create an asymmetrical look by taking chunks out from a design, trim on the diagonal, use the pattern to create an edge but cutting out various blocks.
Diecut papers came in a couple sizes - 12 x 12 and 8 1/2 x 11", but there were some that were also larger than a journaling card, but smaller than 6 x 6. These are probably the easiest to incorporate. Make them journaling cards (as seen in the layout from PageMaps above.) Mat photos. Use them to create layers. You can follow the same advice as when using a larger size - cut them in half, trim and use the edges.
I've been inspired. Now I want to toss everything I have on my plate today and go dig out some of those diecut papers I refuse to give up and use them.