Earbuds are normally worn to allow non-TSO ANR headsets to be used in operations which require TSO headsets.
If you want to reduce ambient noise, earplugs do help with that, you just turn up the audio panel volume up as needed so you can hear the radios or whatever you're listening to through the earplugs.
Might be a problem for stall, gear horns on GA planes. On transport planes, airplane aural warnings are typically routed through the headset audio as well as the cockpit speakers for that reason.