Here are some things I've noticed about this, at least in the "free" tier web models since that's all I typically need.
* ChatGPT has never denied a response but I notice the output slows down during increased demand. I'd rather have a good quality response that takes longer than no response. After reaching the limit, the model quality is reduced and there's a message indicating when you can resume using the better model.
* Claude will pop-up messages like "due to unexpected demand..." and will either downgrade to Haiku or reject the request altogether. I've even observed Claude yanking responses back, it will be mid-way through a function and it just disappears and asks to try again later. Like ChatGPT, eventually there's a message about your quota freeing up at a later time.
* Copilot, at least the free tier found on Bing, at least tells you how many responses you can expect in the form of a "1/20" status text. I rarely use Copilot or Bing but it demonstrates it's totally possible to show this kind of status to the user - ChatGPT and Claude just prefer to slow down, drop model size, or reject the request.
It makes sense that the limits are dynamic though. The services likely have a somewhat fixed capacity but demand will ebb and flow, so it makes sense to expand/contact availability on free tiers and perhaps paid tiers as well.