If the child is happy to stay on her own and not worried or frightened about it, it will be absolutely fine. DC these days are not like generations before who generally needed a lot of parental input to do stuff to prevent boredom. They have loads to do without having to leave home.
Not particularly healthy to be indoors all day but in some ways a safer option than making her attend activities which I assume she has to get to and from herself with no one at home to check she got back on time, went off with people she doesn’t know etc. Can he go for a walk with her after work?
Your DP needs to just ensure she has plenty of food she doesn’t need to cook to eat, reminded not to answer the door at all, and not really to be sleeping while alone in the house as I’d be uncomfortable in case of someone trying to get in if car is not there.
Can he get a video doorbell put up, so he and she see who’s there? Also a good deterrent. DH often answers the door while he’s at work if I’m on a work call or out! Also make sure back of house is secure.
She must have someone to call, if not police emergency, like a family member even if not in same town, who can give advice if she’s worried about anything or just wants to talk to someone.
TBH I’d also say he should explain to his work, he needs to be able to answer texts, take calls if needed as his DD is at home and she needs to be able to reach him. If there wasn’t an issue with this, I would not a problem at all - I’d be video calling over the course of the day and probably annoying the hell out of my DC anyway.