HTTP Cache warmup doesn't do anything, cURL aswell

We have a bit of an issue.
The shop we are working on has a lot of products and properties, which leads to long page load times.
The load times are good once the page has been opened and cached.
The builtin cache warmer doesn’t seem to work, and we tried to open all categories via cURL, that hasn’t worked either.
Cache only gets generated correctly once a real request via a browser has been made, do we miss something?