Nah, I don’t think so. There are shows (usually very good) that wouldn’t be tiresome, yes, there are. Perhaps because they are ambitious shows that successfully achieve what they were aiming at. Or they fall more into a completely story cut in pieces than a proper episodic story. Or they use the curiosity tactic to drive the viewers to keep on watching the show, instead of watching it simply because it’s enjoyable.
It depends on the kind of anime, its purpose, and how the story is handled… For some kinds of show it’s just natural to be tired after watching a lot of episodes in one go, despite being good.
But you can just ignore some episodes that seem not to be worth reflecting about it, and you can end up missing some stuff if you don’t re-watch. You think about the series as a whole, but when you watch weekly you reflect about each episode individually.