Which anime has the most realistic/intricate political intrigue?

Well that's one anime that focuses the most in politics. Some of the mecha that were mentioned there seemed to do as well from the descriptions and reviews I've seen. But if LOGH didn't satisfy you in that regard than I don't see how anything else in the medium would.

Maybe try historical mangas or anime or court room palace series? They are usually about that, but I stll don't think you would be pleased in that regard.

If you don't mind palace intrigue slash mystery without the sweeping scope of a space opera, Yatagarsu is a good watch.

In fantasy ancient Japan, four bridal candidates enter the palace in the hope of marrying the prince, as their respective houses compete against each other for dominance. And there are many in the shadows that just want the prince dead. We follow the prince's new attendant through the story as he tries to make sense of all of this and hopefully not get killed.

@tchitchouan I literally thought of this one when I saw the title of the post. But they say that LOGH is something they watched and it didn't live up to their expectations.

IDK I don't think there is a great series for it. I would say in terms of grounded politics, I actually thought GITS SAC did a pretty good job showing off an immigration crisis (that sub plot is kinda funny now considering who is currently running Japan). That said, there isn't a lot of anime, I would point to that is like IDK realistic. LOTGH is a pretty general take on history/politics. The Empire is a good very general take on say Napoleon's rise to power, and the FPA a good take on the dangers liberal democracies can find themselves in, however, it's not in depth for me to define it as "realistic".

If there is an anime equivalent to West Wing or something, let me know.

I wouldn't go that far. Despite LOTGH being my favorite anime, I actually do agree that after EP 87 it loses it's steam a bit. That said, I actually do like how everything is totally resolved, and it does I think give resolution to both political views, even though Tanaka is still favoring liberal democracy by the end.