Would you say this is no more than some obvious ego stroking, as well as a sadistic game like a cat playing with its food before eating?
Pretty much this, yes.
I don't like how random many of the cases feel. There's a lot of butting in on crimes committed outside our jurisdiction, with no explanation given and no consequences. Sure, we're pretty much in Ferelden's and Orlais' good books as the story progresses, and I can see the locals asking for our judgment because the proper authorities are absent or uncaring. It's not like I mind bringing justice where people couldn't otherwise expect it. But I do want there to be explanations and consequences. Plus, some cases just make no sense to me:
Knight-Captain Denam/Alexius? He was apparently stuffed in a portable hole for months on end, because that's the only way I can see him make it from the recruitment mission until Skyhold is refurbished. He should have been dealt with on the spot instead. With Alexius, there's even the added bonus of the proper local authority showing up at the right moment.
Erimond? There's no bloody way he's still alive for a trial -- hell, there's most likely not even a body left. First Clarel kicks the ever-loving crap out of him, then the lyrium dragon tramples all over the place, then the wall collapses and we fall into the Fade. The guy is nothing more than a finely-ground red paste floating through the Fade, and good riddance.
Florianne? Orlais' ruler is still in a tenuous position and could really do with a show of power to solidify their claim. Handing over the person who committed high treason is an admission of weakness they can't afford.
The only cases that really make sense to me are Blackwall and Ser Ruth. (Though with her there's still the question of which utter nitwit let a Grey Warden mage into my fortress, even as a prisoner. Probably the same nitwit that lets the other Wardens prance around the place. None of them should be allowed within ten miles of Skyhold or the Inquisitor until Corpyheus is safely and permanently dead.) She literally asks for it, and if we want to judge him we need to get him away from the local authorities first.