Brushless motors are used all over industry
They are, but more routinely using AC. Some of the more interesting DC motors use masses of electronics (eg the so-called "Switched Reluctance (SR) Drive) to improve efficiency, but possibly making them difficult to get certified for aircraft use.
The key issues for an electric aeroplane are likely to be energy density of power sources and airframe efficiency. Energy recovery, in-flight generation and reliability may have a part to play, but until the first two are cracked, routine powered flight of significant duration is inevitably limited (though motor-gliding is another matter).
I don't agree that the noted factors afflicting light aircraft petrol engines are
actually non-issues
. Too often do we see the probable cause of a crash as "probable carburetor icing" - something that modern automotive engines have long ago left behind. On the other hand, GA engineers are - quite rightly - a conservative bunch and it can be instructive to look at the more and less reliable LAA engine installations to see that car technology doesn't always transfer happily into the air.