Well, here the op again.
I wondered what reactions would be and what other mother/parents would do and find acceptable regarding their children. What I learned here is that, as I personally was thinking as well, is that it mostly really depends on the child and not so much the age. My thinking actually shifted from 'age- appropriate' to 'child-appropriate' and this shifting happened through my own 7yo. Personally I would never feel comfortable to leave a 3yo at home alone for even a short while (or my youngest, not even in a room alone at that age ;-), nor at 4, 0r 5 for that matter, unless asleep and myself just being in the front or back yard with my other child (and the sleeping child within hearing distance and with regular checking in). But now my eldest reached the age of seven and I felt things shifting and I felt I needed to adjust my thinking, to look further than age and more at personal needs and abilities. His needs were obviously changing. He started to have the need to be able to be alone for a (short) while and he started to feel annoyed with the daily errands when he had to accompany me and his little brother. My need was for him to be ok and to be safe and for the 3 of us to be comfortable. His needs have been shifting and even though I felt a bit awkward about a '7' year old to stay at home for a while (speaking about 15 to 30 minutes here, not longer) I felt him to be ready and capable of an occasional staying at home. So I listened to his needs, he listened to mine, we made a deal that he could choose a maximum 1 or 2 times a week where he wouldn't come along bringing his brother to school, and but) the other 3 days their would be no need for resisting or nagging or stress from either side on him accompanying us. And he would also need to know what to do (and what not) during the time I would be out. So far, this is working great. He feels respected in his new need, and I do feel so in mine (I'm not comfortable doing this every single day yet so the deal of 0-2 a week is fine by me). He knows how to contact me and use the phone, he knows which neighbour he can go to in case of emergency, he knows how to open or lock the doors, he is under no circumstance allowed to open the frontdoor to ANYONE except mom or dad (we did test this as well ;-), he knows to pick up the phone when it's me and not to when it is another number, and he knows what to do best in case of fire or earthquake, and he knows what he is very aware of the 'hazards' in a regular home (like stove, electricity, tools etc.) . And usually he does his homework, reads a book or watches some tv. So this is my firstborn. However, looking at my ds of 5, his abilities and his character, I am not really sure if at 7 HE will be capable of doing the same and I suspect it will take a little while longer for him to reach the level of maturity and trust (regarding safety) it takes to stay at home alone for 30 minutes. And I would not go anywhere than by walking distance within max. 10-15 min. from home. I would NOT let my 7yo stay home for longer periods so far, nor would I leave him alone more than the present maximum we agreed on. That may change in the future, after discussion and mutual consent.
I see the above seems more like an exception than standard looking at all the reactions. But I also see there are others in the same situation who have a child they trust to be able to do this. And I understand every single one reaction comes from a whole personal set of experiences and elements, and so they're all different.
I know parents who've left their (very young) children at home for a while without really thinking it over, however, I do think it's not something you do 'just like that'. But it's so much about KNOWING your child that makes you able to come to such a shift or decision, and sometimes this shift may happen so fast you don't even notice and sometimes this may take much much longer. It also depends a lot on the parent, the bond, the trust involved from both sides, the environment, it's a whole package to look at, not just age, not just mere ability or responsibility. If the decision to leave a child alone for a while stems from well thought of, responsible parenting, and if the child agrees with the situation, it is imo, responsible.
I would NEVER (at least, not yet, and not for a LONG time) leave my two children home alone at these ages, because that, for sure, wouldn't work and wouldn't be safe. Not in the near or not so near future either. I trust that one day that shift will come true and thy will be up to this particular responsibility.
I started to wonder about the 'alone' idea, too, because I bring my child to school a little earlier (as some others do, too) to pick up his little brother in time to from (another) school. This means the 7yo will be 'alone' (not really ;-) in the school yard for about 15 minutes (unfortunately one day I got scolded (!!!) for this by someone who obviously didn't think it was something to be done). However, I find this pretty normal for a 7 year old who is very fine with that arrangement. Then, many other parents or grandparents, (in my eyes then again 'helicopter(grand)parents') stay in the school yard until the kids disappear in the schoolbuilding with their teacher (which I find pretty weird actually for children aged 7-12 years old). Actually, I would be more comfortable if those adults would NOT stay on school grounds after bringing their child(ren), and would be able to trust the schoolgrounds enough for their children (age 7 and up) to be ok, since they also won't be there sitting next to their child in the school benches for the next couple of hours nor during the breaks. And it's not really like they all are watching their children closely while waiting there.
But well, other people, other perspectives just as in the above.