Some callers of content::CreateFileURLLoader() can tolerate BEST_EFFORT TaskPriority, but others cannot. content::CreateFileURLLoaderFactory(), and possibly other code also needs to be looked at. To be clear, it seems that file downloads can be BEST_EFFORT, but file loads related to proper browser behavior (e.g., loading an extension) need USER_VISIBLE priority.
Background story: I will soon be committing a change that adds a test (NoBestEffortTasksBrowserTest.LoadExtensionAndSendMessages, run via browser_tests) to ensure browser extensions can be loaded and interact with a page even if all BEST_EFFORT tasks are never run. Without patching content::CreateFileURLLoader(), the test passes without the NetworkService enabled, but fails with --enable-features=NetworkService.
Upon investigating, the root cause was the use of a BEST_EFFORT task runner to create/start the load. The file being loaded was the extension's background.js file, and so this never occurred, and caused the test to time-out. My code change will upgrade the task priority to USER_VISIBLE since the loading of the extension's background page should have that priority (see bug 177163 and commit 6cafda46a6a41b3f857846e3d1e2e9ae8739ed2e for further discussion).