Well, Vinnie, as you can imagine, that is a question I have pondered myself. Why would they let Oswald wander around freely in the 45 minutes before the shooting? Wouldn't it have been much better for them to tell him to lay low somewhere? To stay out of sight? To hide?
Yes, it would have been much better for them if he had done that. However, what reason could they have given him to do it? If I'm right that Oswald didn't know anything (and I am) then how would it have worked if they told him,
"Listen, Lee, we need you to stay out of sight during the lunch break and during the motorcade. We don't want anyone to see you. So, go on up to the 3rd floor and wait there."
What's he going to say? Isn't he going to ask, "Why?" And knowing that he could be arrested afterwards and vigorously questioned by police, what if he told police, "Mr. X told me to go hide during the lunch break." Wouldn't police want to talk to Mr. X? So, my thinking is that they watched him constantly during the lunch break, and they had people in the doorway (particularly Bill Shelley) to make sure that if he didn't advance beyond the landing if he went out. But, that's it. Otherwise, they took their chances on people seeing him. And I think they figured that they could always intimidate those witnesses and, if necessary, marginalize them. The important thing was to not tip Oswald off about what was really going on. They could not empower their patsy with knowledge that he could use against them when in police custody.