Putting him in the open world wouldn't change anything, it would be posted within minutes. And even more lazy people would be asking for an app to buy things from him because even the simplest tasks are too much for their lazy, soft, a.d.d. , pampered behinds to do.
Putting him at the end of a mission would be even more complicated. First off you would have to have your coins and motes with you, plus if you are upgrading armor or weapons you need them with you. What happens if you can't find someone to do the nightfall with you or you are doing the weekly heroic and the matchmaking sucks and you have constant afk and/or deaths.
In short, it's a horrible idea that doesn't fix anything only has possibilities to make it worse. Xur is fine the way he is. The only thing I would change is instead of coming once a week for 48 hours he should come for two non-sequential days like Wednesday and Saturday for just 24 hours each. Change up inventory each time. Would make you think if you wanted to spend your coins earlier or wait for the weekend. But he is fine as is.
I wasn't looking to really fix anything besides make it more like a hunt for treasure. I highly doubt he'd be found in minutes. The world's are far too large for that speed. Ending of nightfall might be an issues but not in match made weekly's. Also the app can bring you your gear and coins so that's a non issue.
I'm just spit balling here trying to be creative and give people more reasons to explore every nook and cranny of the world's
Again I would leave Xur alone and they should come up with other reasons to explore. The gold chest weren't worth it, the dead ghost weren't either. How about something with a reward? Sparrow parts to build an exotic sparrow? Have the locations change with the reset.