No, YANBU.
I had a similar situation. BF and I eventually (and I do mean eventually, could be years off yet, dependent on the situation with our dc) plan to live together.
He was similar to your BF. Separated 7 years, friends with the ex, no shares assets, but still married.
I was concerned there was an emotional attachment that neither would acknowledge. Or it represented something they couldn’t go through with. Or that he was afraid or too guilty.
So I told him he needed to sort it out, that hell would freeze over before I move in with someone else’s husband!
He has now sorted it and the divorce is nearly finalised. It was very easy. They filled in a few forms, paid the money and that was that.
I would imagine there is some emotional connection left over. Your relationship is not a level playing field. You shouldn’t normally issue ultimatums but I would say if he doesn’t do it, know you are not his priority and leave the relationship.
If it’s not a big deal then why hasnt he done it?