Why couldn't they save this ship by running it aground?

“It has been speculated that the deep, almost vertical shore of the bathtub-like caldera made it impossible to beach the ship and save her from becoming a total loss.” from this Wikipedia article.

Considering that it took hours for her to founder past the point of moving or salvaging, and they certainly had the passengers and nonessential crew off in plenty of time… I don’t get it, either. It’s not like they had to ground her “right there” ... it seems like they had about 4–6 hours to move her somewhere else.

Yeah. My thoughts exactly!

Moving a ship that size whose hull has been seriously breached below the water line any distance is almost impossible, as towing hastens the process of water entering the hull. Bringing in the equipment to implement patching takes time, and depending on the size of the hole(s) in the hull, may not be at all feasible.

Watch the video… They moved it around that bay quite a bit whilst it was sinking…

I did watch the video, and saw a bunch of different camera angles, and no evidence that ”they moved it around that bay quite a bit whilst it was sinking…” In a situation like that, evacuation of passengers and preventing loss of life is the first priority. Movement around the bay was probably more due to tidal and wind influences. The shape of the caldera itself has an impact on movement of water. Nowhere did I see anything that indicated where the nearest beach or appropriate grounding area would be.
Oh, wait. Is this a trick question? Your “source” being a YouTube video with nice music should have been my first clue. Oh, silly me, I honestly thought you really wanted to know why.

For those interested, this addresses possible options to avoid future incidents of this sort.

Why do there have to be mean-spirited people in the world who take out their anger at random strangers?

I would think that if it gently sank in those calm waters there actually might have been less damage than might have been caused by running it aground. I would guess that after some underwater patching they could raise it with straps, airbags, and a lot of pumping.

That seems unlikely, as the caldera is quite deep. But maybe you have a point there…