Keeping a tup with the flock year round can work, but unless you breed all your ewe lambs as hoggs, you do need to be able to separate ewe lambs off at tupping time.
It doesn’t necessarily mean a very protracted lambing. I kept a Shetland tup with my mixed flock and lambing lasted four weeks on average, pretty much never longer than five weeks. Shetlands and other primitives, in my experience of doing this in the north of England, don’t come cycling until late October, and a healthy flock with a healthy tup should give you 95% of your lambings in the first cycle (so lambing over three weeks or less) with the stragglers usually within a week to ten days of that. And, again in my own experience, left to their own devices a ewe often lambs on the same day she was born, and on that same day year after year, so if you only retain those born and lambing in the 95%, your lambings will tighten up year on year.
Some tups can be a nuisance with lambs, but many aren’t - quite the reverse, some become guardians of the flock and are gentle with the lambs; we named one such Dutch Texel “Big Daddy” because of how lovely he was with the lambs. My experience is that giddy ewe hoggs cause far more upset at lambing time! I lost a pregnant ewe because of it once, so I don’t now run my hoggs with the lambers until lambing itself has finished and all lambs are at least a week old. The hoggs still get to see young lambs but aren’t around to cause angst when the mums are actually lambing or in the first few days when the mums are super-protective.
And I’d probably keep a new tup in the field next door from about one month out and until the youngest lambs are a week old for the first time he’s present during lambing.
As to keeping a tup with wethers for company, it doesn’t always work. Chad had been used to staying with the flock year round, and when we separated him after tupping the first year here in Cornwall, even though he knew his 4 companion wethers really well, he simply couldn’t settle. We’d expected to keep him a while to put condition back on (that was his third year tupping and there would be daughters entering the flock the following year), but he was so unhappy we just sent him off. We had him minced in case he was still tuppy, but in fact the meat was some of the best we’d ever eaten!
My other comment is, if you’re going to keep a tup and keep him separate apart from tupping time, then if you’ve got the paddock to do it, keep two or three wethers for companions, not just one, then they’re still a group while the tup is working. And if you can and his happiness matters to you, don’t make it always wether
lambs he has for company - let him have a pal or two that stay on year on year, so he has adult company.
(Yes, you could say our sheep are spoiled

. We prefer to say that their welfare - physical and emotional - is paramount to us.

. )