Back in the mid 90’s, I was looking at unmounted stamps for the first time, but buying all sorts of wood mounts separately didn’t seem to be that cost-effective so I wasn’t doing it. That changed when HALOS (Hooked and Looped On Stamps) came up on the stamping mailing list I was on.
I had already tried using Velcro but found it difficult to use and found that the stamps wobbled too much on the mount I had covered in hook tape and taking the stamp off required a lot of tugging. HALOS, on the other hand, sold acrylic mounts with channels ground into them so you had one, two or three strips of hook tape in the channels instead of all over the stamp. This allowed the stamp mounted on loop tape to stick to the mount, not wobble so much, and removing it was much, much easier.
I went crazy after that mounting things on this system and even converted a lot of my wood mounted stamps to this system. There were two major down sides to this, though. My KAI scissors would get gummed up with the ultra-sticky adhesive on the loop tape requiring frequent cleaning, and cutting the stamps out would create little fuzzies all over the place as some loops of the loop tape got severed from the tape. Had to do a lot of sweeping those days.
Eventually I started having trouble with the adhesive on the tape itself hardening and then turning to powder forcing me to remount a lot of my dies and I took a break from repositionable stamp systems.
Yes, I have cling mounted stamps as well, and have also had trouble with stamps sliding off the cushion as the adhesive degrades over time, so no system is perfect. But I still have some of these dies on Velcro that I haven’t remounted and really should at some point.