Take a look at data virtualization. It's an alternative to data warehousing without the burden of making mutiple copies of the data; instead, it retrieves the information fron source systems in real time.
The "single view of customer" use case, which is the one you mention in your post, is one of the oldest that this technology aimed to solve and it does solve it very well.
Does this actually work though? For instance, we may have user data in an API that, thanks to arbitrary rate limits, isn't useful at all when querying in real time.
You mean not being able to access specific user data due to hitting the rate limits of the API? In that case, you can always cache the data (using the cache facilities of the data virtualization layer) and create a hybrid real time/cached workflow that pulls data in real time when possible and from cache for the APIs that have restrictions in place.
The "single view of customer" use case, which is the one you mention in your post, is one of the oldest that this technology aimed to solve and it does solve it very well.
Disclaimer: I work for Denodo (http://denodo.com).