Why would cardiologist did not suggest a defibrillator?

This is only a thought, you must clarify with your cardiologist.
Perhaps because a defibrillator will not be effective for you with a low EF which indicates heart failure - not a potentially fatal arrhythmia which could be reserved back to normal rhythm with an internal defibrillator.
And a note: My mother lived to 88 and was in and out of heart failure. Her EF went as low as 20%...and my feeling is if she did not fracture her hip would have lived to 90.
So, don't despair over the %. There are many, many medication options to treat heart failure and you can have a very good quality of life despite a low EF.
The very best to you.