Prisons have to be resistant to the attempts of their occupants to escape, or to cause damage or destruction. This doesn't really seem compatible with warm and inviting.
Most prisoners don't want to escape, or cause harm, they just want to finish the term and go home and move on. I'd say you could have the honor system (unlocked doors) for 95 percent of prisoners, by letting them know if they escape they'll go to a more secure and less free prison. Then you make prison a place to learn new skills and get treatment for addictions and therapy, and you'll actually see some improvement in society. Also, send less people to prison.
We already have prisons like that for low-risk, nonviolent offenders. They are called minimum security or "country club" prisons. We also have home detention.
In America that's so rare it's nonexistent. A few rich white collar criminals might get home detention, but for most people who have the option, it's too expensive, with fees of hundreds of dollars a month or more. Country club prisons aren't a real thing, that's just talking points for the "tough on crime" politicians who want to make prison sound fun.
They can be. If you're curious, check out "worlds toughest prisons" on Netflix, an episode that shows a Norwegian rehabilitation-focused prison. You can see how the place is both secure and warm.
I've seen pictures of Norwegian prisons. They certainly look comfortable, but I wouldn't describe them as "open, warm, and inviting". They look halfway between a no-frills dorm and the psychiatric ward I stayed in for a while as a teenager. Certainly far more humane than American prisons, but still clearly _institutional_.
