A quiet line test should be quiet. End of.
If you have a phone that makes noise when none exists then get a new phone.
Conduct the test in a quiet area. If you can hear traffic or a hoover then conduct the test at a quieter time of the day, or simply listen for noises on the QLT that you can't hear prior to making the call.
A cheap £5 corded handset from Argos is absolutely quiet during a quiet line test. Not a buzz, hum, click to be seen. If any buzzes, hums, clicks (or any Electrical noise) can be heard then it suggests an issue and should be reported to the voice provider.
That's why it exists and why it's called a quiet line test. No lab necessary.
If you have hearing difficulties then obviously a quiet line test is a useless exercise.
You aren't conducting scientific experiments. You're listening for a noise during a call that you couldn't hear before the call.
Issues/noises that show up on a QLT are usually distinctive. Persistent buzzing, repetitive clicking, crackling noises, etc. You aren't listening for tiny noises that require an anechoic chamber.
To add, the pilot tone being missing is a red herring. It can also move tones as well as not show at all.