I can think of absolutely no reason why beans, or tinned spaghetti, prunes or peaches should not be served with a cooked breakfast, if that is what someone wants, A fried breakfast is really just a random collection of food that will cook in a frying pan.
The modern cooked breakfast is just that, a modern recreation of a meal that never existed in its current form. As a child a cooked breakfast meant a fried egg, a rasher of bacon OR a suasage and a small piece of fried bread and no more.
Yes, a Yorkshire pudding customarily went with roast beef in Yorkshire. If you want to be purist, it should not be served outside Yorkshire. Elsewhere all joints were served with a boiled pudding of some kind, or to be precise the pudding (including Yorkshire) was served before the meat.
If you read Charlotte Bronte's novel Shirley the squire in there says to one of his children 'No pudding without broth, no meat without pudding.' meaning you had a bowl of soup and then a slice of pudding to be eaten before you got to the point in the meal where you were served meat. The first two courses blunted your apetite so that a small quantity of meat could give a satisfactory meal to a large family.
Both meals, a modern cooked breakfast or roast beef with a yorkshire pudding are essentially entirely modern adaptions of traditional meals So eat what you like with whatever you like and only follow the so called 'rules' if you want to.