System-Wide Flask Installation
The problem comes mainly if you want to run multiple different applications/projects, they would need to use the exact same version of flask and its dependencies. Anything else would cause conflict among the libraries.
There's also ease of packaging for each application, by installing only what you need for the current application in the virtualenv, it acts as a delimiter (for instance, when using pip freeze --local) so you don't include global packages you might not need.
The principle of least privilege might come into play as well. It would be rare for even global libraries to go beyond their scope but, hey, reducing the attack surface only to what your virtualenv is can't hurt.
The Flask documentation describes how to install it either inside a virtualenv or system-wide. The documentation for a system-wide installation states

This is possible as well, though I do not recommend it.

Why is a system-wide installation not recommend? What problems can occur with such an installation?