I had a TAH with a big vertical incision and I found that I was way more mobile than I had anticipated. I don't have a memory foam mattress, mind you, but it's been fairly easy getting up and out of bed or off the couch, no matter what height or softness.

They told me in the hospital to first roll onto your side, get your legs over the edge, and then use your arms to push yourself up. Standing up was fine, as using my legs didn't seem to disturb my belly.
Same as using the toilet, I was worried I'd need assistance, but I was ok to stand up and sit down with only minimal use of the counter beside me.