For an 8 foot span I'd be concerned that the 1" 80/20 wouldn't be rigid enough w/o adding some structural features that turn them into a truss. If a single extrusion is what is desired I'd go with one of the bigger sizes.
For a 6 foot span it would be more dependent on how much weight was being attached and where it was being attached. If the weight is near the jack brackets it's likely not an issue. If the weight is attached mid-span then it likely either needs to be bigger or it needs a constructed truss too.
Very good point. I should qualify my experience as working well for traction mats, which are a distributed load, over a 6' span. If you have a heavier load, particularly as a point load in the middle of an 8' span, then you may need beefier extrusions. They do make a 1x2" profile which could work well if 1"x1" isn't up to the task: https://8020.net/shop/1020.html