I think the only real benefit to the paper cells is for large-scale growers because they can be loaded into those automatic transplanters. I don't think they'd really have any advantages for the home gardener, and there are probably better options for you.
What kinds of problems were you having with transplanting? I was always taught to transplant in the late afternoon/ evening, be careful not to damage the
roots, and
water them in well. It's always been very problem-free for me this way.
Is there a reason why small plastic pots or 6-packs wouldn't work well for you?
Another option is toilet-paper and paper-towel rolls. You can cut 2-3 little bottomless cardboard planters from each toilet paper roll, pack them in to support eachother in a tray, and fill with soil. They save a lot of space, compared to larger plastic pots. This can be important if you are starting seeds under
lights or something and want to start a lot of seeds in a small amount of space.
You can also make your own paper pots out of newspaper or brown paper bags. I did it before by folding the newspaper around a can of beans as a mold, but for smaller pots you'd have to find a smaller cylinder to use as a mold, like a small piece of pipe or something. It did require a few pieces of tape for me to hold them together, but I'm sure someone handier than I could fold them in such a way that they stay put as they are.
Peat pellets also save space, but of
course peat moss is ecologically problematic, and I find peat pellets a real hassle to use anyway.
I've never tried soil blocks. There is some investment there, and a learning curve with getting the soil right, and I have just never been up to the challenge so far.