I just worked on a Shop Fox dual drum sander for a customer, and it had hook and loop sand paper on both drums. The hook side was attached to the drum by Some type of double sided tape. I would think self stick material would have been better than the double sided tape. I don't know how well it actually works, but my customer said he hasn't had any issues with the paper being a problam...being spongy shouldn't be a problem either, you have to remember it's a sander not a planer.
Hook and loop is how the Woodmaster drum sanders are built. Mine does not seem too spongy . I would caution you not to try taking too big a bite or you may overheat the velcro on the drum and cause the adhesive to turn loose. The rep from Woodmaster advised "these things work in thousandths not sixteenths. If you can hear the drum working you are still sanding, so you may make several passes at the same setting.
I have a Grizzly with hook and loop and a Delta without. The Grizzly is "spongy". It is not that noticeable on most projects. I cut my own veneers and it is very noticeable after I sand veneers. The Grizzly was purchased to replace the old Delta, but I now keep the delta to and the veneers with.