For example, after 19:00 sometime (GMT+1), the response quality of both OpenAI and Anthropic (their hosted UIs) seems to drop off a cliff. If I try literally the same prompt the around 10:00 next morning, I get a lot better results.
I'm guessing there is so much personalization and other things going on, that two users will almost never have the same experience even with the same tools, models, endpoints and so on.
You say the outputs "seem" to drop off at a certain time of day, but how would you even know? It might just be a statistical coincidence, or someone else might look at your "bad" responses and judge them to be pretty good actually, or there might be zero statistical significance to anything and you're just seeing shapes in the clouds.
Or you could be absolutely right. Who knows?