This is a common misconception. Our two Cockatiels are still bonded to us. We have one female Sun Conure who is friends with our Cockatiels, but is still bonded to us. Although we only have one Conure, I have met or seen multiple owners with at least two, and there is still a bond. Some examples from YouTube are BirdNerdSophie, SharynZoo, and FlyingFids - all of them have two or more Conures.
We also have Budgies and our experience has been a lot like what DonnaBudgie described. Most of them are still interested in sitting on our hands, looking at us, chirping and bobbing their heads at us, etc. (Only one, Aspen, is somewhat distant...but she is Basil's lady friend, so we accept that we are providing a home for a bird who Basil likes. And she is starting to take food from my hands more often.)
I think there are benefits to having at least two birds. If one tries something new, such as accepting a treat from you, they can set an example for the other(s). This happened with our Cockatiels. Pepper tried most things first, such as stepping onto our hands. Kona would eventually do it after watching Pepper several times.
Also, the bird will have a companion whenever humans are not home!