A ewe will sometimes go to a lamb that isn't hers that's in distress, but the ewes aren't going to make sure that the orphans are safe, show them where to hide, gather them up if the flock is moving, and so on.
So on our sort of ground, orphans wouldn't last long out with the flock when they're very young. Not to mention how frightening it would be for them if there was a threat - a walker with a loose dog, for instance - and they don't have a mummy to run to for security and comfort.
If a ewe dies, when the lambs are say 6 weeks old, we might leave the lambs with the flock. They already know how the flock works, where to be safe, where to shelter, and so on. But bottle-reared orphans haven't learned all this.
Another consideration is whether the orphans might start pinching milk from the ewes. It starts with them copying their new friends, and the next thing you know is that the mothered lambs are going short, and/or the ewes are getting thin, or mastitis, because the orphans are routinely stealing milk when their pals get a feed.
A mother will teach her lamb about eating grass, won't let it gorge and bloat.
And so on.
Having said all of which, if you have a setup where you can get the orphans back in for the night, which is safe for them during the day, and you can watch for signs of pinching milk and change the regime if that starts to happen, well then yes it's nicer for them to be able to run about with other lambs. But from maybe 4 weeks old, not at a week old, and introduce them to grass gradually. I'd be worried about them eating too much grass and bloating younger than that. A mothered lamb is getting milk little and often, so doesn't get so hungry between meals that it eats too much grass. A bottle-fed lamb will get hungry between meals and is therefore likely to eat too much grass for its developing rumen.
My 5 week old pets are on 3-4 hours a day out on poor grass at the moment, just starting to be let onto slightly better grass now. I'll have them out most of the day in another few days, if we get the weather for it. The 3 week olds are getting supervised walks / play out on grass when I have the time, just for maybe 20 minutes.