I've had my 2 budgies for over two years now and they have never come out of the cage without freaking out. I have a large flight cage for them with many toys, they have very good diets, and they are healthy and happy.
One of my parakeets, Cosmo, will step up onto my finger most of the time. My other parakeet, Lulu, will step up with the incentive of food.
Cosmo and Lulu will exit the cage if they remain very close to it or on top of it, and have millet.
How can I encourage them to come out of the cage and enjoy it? I have tried putting perches outside, putting their favorite toys outside, but the only way is to keep feeding them millet which is not healthy or sustainable.
I don't think they are scared of me, because Cosmo lets me pet her when she's inside the cage and she lets me kiss her tummy. Lulu doesn't feel comfortable with that but I know she isn't scared of me.
Is there any other way to help them get out of the cage? I just feel like despite the large flight cage, they should be out of the cage sometimes too.
Look around the space where the birds are kept and try to access if there is anything in the area that might make them uncomfortable when out of the cage. You have to look at this from the birds point of view because things that are normal and usual to us may not be so to the birds. If there are other people and/or pets around making the area uncomfortable by too much noise and activity they may not want to come out of the cage. You just have to take it at their pace. If they will step up onto a perch you could try having them step up in the cage and slowly bring them out and place them on top of the cage and if they go back into the cage just let them be where they are comfortable.
I would also recommend putting a small playground area on top of the cage. Put a couple of favorite toys and maybe a treat on the playground.
Don't try to force Coco and Lulu out of their safe environment, it should be their decision to come out if/when they are comfortable doing so.
Cody's suggestion of allowing them to step up in the cage and then seeing if they are comfortable being placed on top of the cage is spot on!