When reading and learning about the gold foil experiment, the alpha particles mostly go straight through the gold foil and some get deflected or bounce back but it doesn't say anything about the direction of the alpha particle emitter. Did the alpha particle emitter stay in the same spot or get directed to different areas of the foil? How could they all hit the same spot and get deflected in so many different directions?
Even a small beam is very big compared to a gold atom
It seems you are making an assumption that, if the beam were perfectly focussed it would always show the same deflection (because geometry).
But whatever level of focus Rutherford could achieve with alpha particles, the scale is all wrong for this to be true. Even if the beam was only micrometers wide (very tight for the early technology of the day) it would be more than 10,000 times wider than a single gold atom. And, since the nucleus is what actually scattered the alpha particles, there is another factor of 10,000 or so in scale to consider since the nucleus is very much smaller than the atom.
So the question makes a false assumption. The focus of the macroscopic beam is irrelevant and can never, given reasonable technology, come close to focussing on single nucleus. The beam area in Rutherford's experiment will cover vast numbers of atoms and will hit them at random.