I don't consider context a clear win. I'd argue that there's also quite the disconnect sometimes between what a work is about and why it's popular.
Let's take Zombie by The Cranberries as an example. I really liked this song as a kid, still do, I think it has a great sound. The difference is that I now speak English, can understand the lyrics, and could look up the historical context. Ever since I did so, listening to it has never been the same, and not in a good way.
There are also examples which are not going to be so specific to my opinions. Kendrick's Swimming Pools was a house party staple, despite the song carrying heavy anti-alcoholism messaging. The contrast is almost comical.
For a different example, let's consider temporal contextuality; you describe Guernica being reliant on this. When I try to think of an example, I'm reminded of vague memories of shows with oddly timely subtitles. Subtitles that referenced things that were very specific to the given cultural moment, basically memes, but vanished since. It's not a good experience, and I'd say it would be reasonable to chalk such a thing up as a critique, rather than something worthy of praise.
This is also why I half-seriously referred to the piece being "aggressively pretentious". Rather than coming across as something I'm just genuinely missing the context for, it comes across as something with manufactured sophistication (which then I am indeed missing the context for, but unapologetically). This might still be a mirage, but I think with how pretty much stereotyped this experience is at this point, I'd imagine there's got to be some truth to it at least.