I think it very much depends on the stallion, the facility, and the people handling him. As long as there is full disclosure up front, and I can see that things are handled properly, it wouldn't bother me at all. I have been both in barns without, and barns with. To be honest, I had more problems with the geldings at the barn with no stud getting out or being aggressive than the three studs at the barn that had them. They were well-behaved and properly trained, and in appropriate fencing.
I have one of my own, and he is turned out with geldings daily, with no problems. Would I introduce a new horse to his pasture, or even the one adjacent? Not without some serious pre-work first. It's all about being a conscientious owner, or BO.
"Keep a leg on each side and your mind in the middle"