I think your criteria for lumping birds in with helicopters is a little tenuous to say the least.
I have yet to see a bird with a giant spinning feather arrangement on his bonce. They have wings like an aeroplane. Admittedly they flap them which, thankfully, does not occur (often) on fixed wing aircraft.
The choice of birds to stop before landing is surely related to their lack of wheels and has nothing to do with a desire to look like a helicopter.
Maybe evolution could solve the wheels problem given another few million years.
BV