He's been charged with Possession Of A Sharpened Sword

That foot-stool story was pushed by Lactantius, a virulent Christian 3rd century “historian.” He was trying hard to sell the elite on converting to Christianity and the story (as well as pile-ons like having molten gold poured in Valerian’s stomach, or getting skinned alive) were pushed to incite the leaders into converting and fighting the infidels.

It may have been, instead, that Valerian’s anti-Christian policies encouraged Lactantius to imagine a humiliating fate for Valerian. “God punishes sinners and heathens by giving them over to terrible fates” sort of thing.

On the whole, though, I regard the idea as plausible - this was the first time any Persian dynasty had captured a Roman Emperor. Certainly the prestige of humiliating a powerful foe, especially coming on the heels of several other victories over the Romans, was attractive to Shapur, whose Sassanid dynasty’s entire raison d’etre was revitalization of Persia against Roman power.

In practice, captured leaders were often ransomed back, or given nice accommodations and stipends in outlying regions so they would be harmlessly sidelined.

Normally, yes, but I think considering that the powers in question are Rome (notoriously grudge-bearing folk, may not want to release a captured Roman leader if your goal is to consolidate power after the war; and certainly you don’t want any of the Emperor’s long-reaching connections smuggling him out either) and Sassanid Persia (new dynasty seeking legitimacy by showing that they are able to challenge and defeat Rome), there’s reason to afford at least some consideration to the story.

That being said, for the exact reasons you described, it is far from certain that that was his fate. I put ’supposedly’ in the explanation, and elsewhere when this story has come up, I bring up the alternative fates Valerian may have experienced. But since the meme references the footstool story directly, I considered it the most important one to mention.