I never remove queen cells. The idea is that bees will start with too old of a larvae. I don't believe that. Neither did these beekeeping greats:
Jay Smith, from Better Queens
"It has been stated by a number of beekeepers who should know better (including myself) that the bees are in such a hurry to rear a queen that they choose larvae too old for best results. later observation has shown the fallacy of this statement and has convinced me that bees do the very best that can be done under existing circumstances.
"The inferior queens caused by using the emergency method is because the bees cannot tear down the tough cells in the old combs lined with cocoons. The result is that the bees fill the worker cells with bee milk floating the larvae out the opening of the cells, then they build a little queen cell pointing downward. The larvae cannot eat the bee milk back in the bottom of the cells with the result that they are not well fed. However, if the colony is strong in bees, are well fed and have new combs, they can rear the best of queens. And please note-- they will never make such a blunder as choosing larvae too old."--Jay Smith
Quinby seems to agree:
"I want new comb for brood, as cells can be worked over out of that, better than from old and tough. New comb must be carefully handled. If none but old comb is to be had, cut the cells down to one fourth inch in depth. The knife must be sharp to leave it smooth and not tear it."--Moses Quinby
C.C. Miller's view of emergency queens
"If it were true, as formerly believed, that queenless bees are in such haste to rear a queen that they will select a larva too old for the purpose, then it would hardly do to wait even nine days. A queen is matured in fifteen days from the time the egg is laid, and is fed throughout her larval lifetime on the same food that is given to a worker-larva during the first three days of its larval existence. So a worker-larva more than three days old, or more than six days from the laying of the egg would be too old for a good queen. If, now, the bees should select a larva more than three days old, the queen would emerge in less than nine days. I think no one has ever known this to occur. Bees do not prefer too old larvae. As a matter of fact bees do not use such poor judgment as to select larvae too old when larvae sufficiently young are present, as I have proven by direct experiment and many observations."--Fifty Years Among the Bees, C.C. Miller
A study:
David C. Gilley, David R. Tarpy, Benjamin B. Land: Effect of queen quality on interactions between workers and dueling queens in honeybee (Apis mellifera L.) colonies
Selection of high-quality queens by the workers during queen development has been demonstrated by Hatch et al. (1999), who found that during emergency queen rearing (the process by which workers rear queens from worker larvae to replace a queen that has died unexpectedly) workers preferentially destroyed queen cells built from older worker larvae. Despite selective behavior by the workers during queen rearing, considerable variation in quality exists among newly emerged adult queens (Eckert 1934; Clarke 1989; Fischer and Maul 1991). This variation in quality among queens gives workers the opportunity to benefit by selecting high quality queens that are fully developed, when the decision will be most accurate.
https://bushfarms.com/beesemergencyqueens.htm