I think it would be good for non-vegetarian to visit a slaughterhouse and kill an animal themselves once. I think it's good to learn and know about stuff you benefit from, and it would probably be very good for people to be aware of these things. But I don't think they should kill any animal they eat any more than I should grow all the lentils I eat. But doing some gardening, yes, that's good. It helps me know what went into my food, plus it's useful skills in case I ever need them.
On the other hand, I do like the idea of people hunting for food better, just like you do. What I mean is I think an animal who is hunted for and eaten has had a good, natural life until the being hunted of course, while an animal raised only to be killed, well, I think it's much worse ethically, not to mention pollution-wise, etc. So while I don't hunt myself, I find it less objectionable than slaughterhouses.
In my opinion, ideally, meat would come from smaller places such as farms, with people who actually know each one of their animals and try to give them a good life, etc. The problem of course is that it requires a smaller scale, which reduces the amount of meat available in the end, which means people would have to eat much less meat. Like maybe once a week or something.
Nowadays I don't really see it happening, but I certainly encourage people to get their meat from local producers rather than big companies if they can afford it (it's also more expensive of course).
I guess a world in which any meat eaten would have been hunted would probably be fine by me too, but that would probably reduce meat consumption even more and I don't think many people would be fine with that.
And yeah, look into how the meat reaches your plate. You know, out of intellectual curiosity at least. If you happen to find it horrifying, it would make sense to change your habits so as not to condone it (by looking at another source, reducing your consumption, etc). If you don't have a problem with it, then there is no contradiction. But ignorance annoys me.
Anyway, bottom line is, I understand your point to some extent, but it's excessive. We live in a society where people buy things from other people and don't do everything on their own. There would be no time for people to obtain their own food, no matter what that food is, because they have their own jobs and personal life already.