Your argument falls flat when a page file can be multi-GB and automatically grow. And if your application admin was competent, memory monitoring would be part of the application monitoring stack.

An application that grows in such a way (besides having backing stores for memory-mapped files, as well) will often perform so poorly that it requires addressing (adding RAM, looking for application faults, etc).

A page file is insurance, one that can last you much longer than available system memory.