"As the queen is capable of adapting the sex of the eggs to the cells, so she is also able to adapt the number of eggs to the requirements of the stock, and to circumstances in general. When a colony is weak and the weather cool and unfavourable she only lays a few hundred eggs daily; but in populous colonies, and when pasture is plentiful, she deposits thousands. Under favourable circumstances a fertile queen lays as many as 3000 eggs a-day; of which any one may convince himself by simply putting a swarm into a hive with empty combs, or inserting empty combs in the brood-nest of a stock, and counting the eggs in the cells some days after."--Jan Dzierzon, Rational Bee-Keeping, 1882 English edition, Pg 18
"We occasionally read in books on bees, or works on natural history, that the queen in her lifetime lays about 60,000 eggs. Such a statement is simply ridiculous; 600,000 to 1,000,000 would be somewhat nearer the truth; for most queens, in spacious hives and in a favourable season, lay 60,000 eggs in a month. The queen, as a rule, commences laying eggs in February, and continues until September, though not always at the same rate. An especially fertile queen in the four years, which on an average she lives, may thus lay over 1,000,000 eggs. The Author once had a queen fully five years old, which was still remarkably vigorous, and might have lived for another year or two if she had not been destroyed. It is, therefore, quite credible that the age of the queen occasionally extends to seven years, as we are assured by some bee-keepers who have made this observation; yet when we are told that in exceptional cases queens have continued alive for eleven to twelve years, the assertion probably rests on a delusion, or such a case is as rare as that of a man attaining the age of one hundred years or more. There is certainly a great difference among queens as regards fertility; the best mothers are those that lay a great number of eggs and deposit them in the cells regularly, neither laying two eggs in one cell nor missing a cell. With such a queen in the hive the brood is nicely arranged, and much of it hatches simultaneously, thus making it easy for the queen to repeat the operation of depositing eggs when the cells have been emptied. When such is the case the stock will be thriving, its well-being depending chiefly on the queen, who, as it were, is the soul of the hive."--Jan Dzierzon, Rational Bee-Keeping, 1882 English edition, Pg 18
"Queen Excluders... are very useful in queen rearing, and in uniting colonies; but for the purpose they are generally used, viz., for confining the queen to the lower hive through the honey season, I have no hesitation in condemning them. As I have gone into this question fully on a previous occasion, I will quote my remarks:--
"The most important point to observe during the honey season in working to secure a maximum crop of honey is to keep down swarming, and the main factors to this end, as I have previously stated, are ample ventilation of the hives, and adequate working-room for the bees. When either or both these conditions are absent, swarming is bound to take place. The free ventilation of a hive containing a strong colony is not so easily secured in the height of the honey season, even under the best conditions, that we can afford to take liberties with it; and when the ventilating--space between the lower and upper boxes is more than half cut off by a queen-excluder, the interior becomes almost unbearable on hot days. The results under such circumstances are that a very large force of bees that should be out working are employed fanning-, both inside and out, and often a considerable part of the colony will be hanging outside the hive in enforced idleness until it is ready to swarm.
"Another evil caused by queen-excluders, and tending to the same end--swarming--is that during a brisk honey-flow the bees will not readily travel through them to deposit their loads of surplus honey in the supers, but do store large quantities in the breeding-combs, and thus block the breeding-space. This is bad enough at any time, but the evil is accentuated when it occurs in the latter part of the season. A good queen gets the credit of laying from two to three thousand eggs per day: supposing she is blocked for a few days, and loses the opportunity of laying, say, from fifteen hundred to two thousand eggs each day, the colony would quickly dwindle down, especially as the average life of the bee in the honey season is only about six weeks.
"For my part I care not where the queen lays--the more bees the more honey. If she lays in some of the super combs it can be readily rectified now and again by putting the brood below, and side combs of honey from the lower box above; some of the emerging brood also may be placed at the side of the upper box to give plenty of room below. I have seen excluders on in the latter part of the season, the queens idle for want of room, and very little brood in the hives, just at a time when it is of very great importance that there should be plenty of young bees emerging."--Isaac Hopkins, The Australasian Bee Manual
http://www.bushfarms.com/beesulbn.htmA lot of the issue of the queen laying in supers is because of a lack of drone comb in the brood nest. The bees don't want to have brood scattered all over, but the need to raise drones is a high priority and they will if they need to. They can tear down comb that has no cocoons in it, and frequently that is the case in the supers, so they go there and make drone comb and the queen lays in it. I ran several FlowHives for several years now. I got the first one a year before they were on the market. I've never used an excluder with them and never had an issue, but I think that is partly because of the drone comb in the rest of the colony. Also the cells are too deep in the Flow frames and not the right diameter for either workers or drones.