When we just had Lexi, she refused to sleep in her crate. She would pee, poop, roll in it- throw it out every corner of the crate and have it all over her all the while shrieking like a woman being murdered. It was so unbelievable that such a cute LITTLE puppy could incessantly make that kind of racket. She eventually won the battle of getting to sleep in the bed… for a while.
If Lexi is crated alone, she used to destroy anything she was close enough to touch. When my husband and his dobie entered the picture, we crated the two dogs together and they LOVED it. Neither would destroy anything and they always used each other for pillows. It was very cute. My parents have our dobie now as we moved to a tiny apt 700 miles away... so we went back to just one dog until last February when we rescued Miles.
Miles howls like MAD when you crate him. He used to pee just by being inside the crate- before you even shut the door. But we have gotten him to the point (with treat training) that he will energetically get in his crate. We haven't gotten him to quit howling after he eats his treat though. Neither dog is destructive in their crates anymore, but I would definitely say that there are a lot of Basenji's with crate anxiety as well as separation anxiety.
I would love to be able to leave our dogs out in the house, but I absolutely would never try it. I did that several years ago with Lexi & the Dobie and it was a very expensive mistake-- bye bye every set of blinds in the house- pulled down and shredded, bye bye entire couch-- back ripped open and all the fluff pulled out, bye bye duvet/comforter--holes galore. But those are just my dogs. So... they get the crate.