Yea, I agree with you fully
Cliffworms, the flavor text in Arena is very well done and I wish this was implemented in the later games, or other games generally for that matter. I remember a similar feature being one of my favorite details about the first two Fallout games, though it isn't nearly as developed and some of it can be easily missed since it only appears in the Pip-Boy display. I also thought Arena had an awesome intro sequence that, while sort of lame visually still fully explains your circumstances and what is expected of you and establishes you in your role seamlessly, while most games from that time tended to just start with no introduction whatsoever or one that was very brief without explaining much of anything.
Take one of the games biggest inspirations for instance - it starts off a Nietzsche quote (yea, that one) and then displays what I imagine must have been an enormous expense, a fully animated prerendered cutscene that shows... like, a mountain and a bird flying around, then a dragonfly sitting atop a rippling pool flapping its wings in the wind. And that's it, you just begin the game. I know that this is the case on the PC version, and that a significant portion of the data files on the disks was this cutscene. I forget if it is similarly animated in the Amiga version, but I know that in the Atari ST version it isn't, you just get a few still shots of the same scenes in sequence.
It seems that around that time, approximately anyway, proper introductory sequences were beginning to be an expected feature as opposed to the player having read the manual, and with CDs offering more storage space it became possible to include such a thing without having to sacrifice more important features. Some games definitely had less-animated but equally as informative and seamless an introductory sequence before Arena, for instance another game it drew massive inspiration from, Ultima Underworld. The cutscene there was brief, but it was sufficient to convey the urgency of your quest and you begin the game with a clear goal in mind. But other games even those that I truly love, like the Might and Magic games, were weak on establishing your reason for being in each world. The Clouds and Xeen and Darkness of Xeen have awesome intros, they are very well animated, beautifully rendered and very funny, but they only give you a minor overview of a bad guy without any details about the environment and history of the lands you are entering. I actually miss PC big boxes for games and the manuals, maps and other materials that they used to come packaged with, and always when I play an older game if I own a physical copy (which I do for several of my favorites, like Darklands, the aforementioned Xeen games as well as Isles of Terra, Dragon Wars, Ultima Underworld, Wizardry 6 and 7 with clue books for both, Daggerfall, the first Dark Sun game, X-COM Apocalypse, a few Gold Boxes, Jagged Alliance and Deadly Games, and a handful of other lesser known games from SSI and such like The Summoning, Prophecy of the Shadow, and a few others) I will get the box out and keep the manual and map next to my laptop for reference and to recapture some of the original experience. If I don't have a physical copy I'll use a digital one instead, and I really love getting the backstory and some of a games lore from within the manuals, but I definitely appreciate it when a game provides an intro to help get you into it, even if it is just a basic dungeon crawler with no major narrative elements. In my opinion Arena really does a great job, and Daggerfall is among my favorite intros off all time. I sometimes randomly say to strangers "...Excuse the gloom, but none may know of this meeting" like at the grocery store lol, just for fun.