I left my 12 year old at home yesterday whilst I went to work as DP had to go to the office for two days, and I couldn't wfh as I normally would. She could have gone to her dad's but didn't want to.
When I got home she'd cleaned the hob, cleaned one of the cupboards, and tidied another. She'd also done her chores. I'm sure she spent a chunk of the day on screens too, and it looked like some crafting went on.
I'm leaving her again today - I have a meeting I can't move. She already has plans for what she wants to do whilst I'm gone. Friday DP will be here so she's made plans to go meet up with friends.
She likes the chance to be alone in the house, and she's capable of entertaining herself (apparently by doing random housework?!) I think many 12 year olds are the same.
That said, it's a different situation to yours because my office is a 5 minute drive away so I can get home if she needs me. My job does have travel but I don't travel unless she's with her dad or DP. DD also isn't allowed to leave the house/garden whilst home alone, so I always know where she is.
My issue wouldn't be with a child being home alone at 12 (obviously, I do it) if they're comfortable with it, and you trust them to follow rules etc. My issue would be with the length of time, the amount of days, and the fact that the dad isn't close by. If my office was further away I wouldn't feel comfortable leaving dd. That said I also wouldn't want dd taking herself to activities.
I suppose my opinion is - it's ok to leave a 12 year old if you're confident they are mature enough, and are happy to be home, but not for more than 8 hours, and only if you're local. Four days a week also feels far too much.